Electronic copy available at: http://ssrn.com/abstract=767125

DO OLDER INVESTORS MAKE

BETTER INVESTMENT DECISIONS?

George M. Korniotis and Alok Kumar∗

Abstract – This paper examines the investment decisions of older individual investors. We find that older

and experienced investors are more likely to follow “rules of thumb” that reflect greater investment

knowledge. However, older investors are less effective in applying their investment knowledge and

exhibit worse investment skill, especially if they are less educated, earn lower income, and belong to

minority racial/ethnic groups. Overall, the adverse effects of aging dominate the positive effects of

experience. These results indicate that older investors’ portfolio decisions reflect greater knowledge

about investing but investment skill deteriorates with age due to the adverse effects of cognitive aging.

(JEL D14, G11, J14)

I. Introduction

The older population in the United States is growing at a dramatic pace and it is also becoming

more diverse in terms of its racial and ethnic composition.1 Because of this growth in the

proportion of older people, there has been heightened interest in understanding their post-

∗Korniotis: Board of Governors of the Federal Reserve System; Kumar: McCombs School of Business, Uni-

versity of Texas at Austin. We would like to thank two anonymous referees, Warren Bailey, Robert Battalio, Jeff

Bergstrand, Sudheer Chava, George Constantinides, Shane Corwin, Tom Cosimano, Alex Edmans, Joe Egan,

Xavier Gabaix, John Griffin, David Hirshleifer, Roger Huang, Mark Hulbert, Zoran Ivkovich, Jerry Langley,

Sonya Lim, Tim Loughran, Alex Michaelides, Fred Mittelstaedt, David Ng, David Pearce, Jim Poterba, Paul

Schultz, Bob Shiller, John Stiver, Paul Tetlock, Stathis Tompaidis, Mitch Warachka, Mark Watson (the editor),

Frank Yu, Eduardo Zambrano, Margaret Zhu, and seminar participants at Notre Dame, University of Amster-

dam, NHH Bergen, BI Norweigian School of Management, and University of Cyprus for helpful discussions and

valuable comments. In addition, we would like to thank Itamar Simonson for making the investor data available

to us and Brad Barber and Terrance Odean for answering numerous questions about the investor database. We

are responsible for all remaining errors and omissions. This paper previously circulated under the title “Does

Investment Skill Decline due to Cognitive Aging or Improve with Experience?”.

1

Electronic copy available at: http://ssrn.com/abstract=767125

retirement quality of life. The popular media has often raised the concern that older people

would not be able to generate the annual income necessary to sustain the pre-retirement quality

of life. Thus, as the U.S. population ages, it becomes important to understand the investment

decisions of older individual investors because investment income is likely to be a significant

proportion of their post-retirement income, and therefore, one of the main determinants of their

post-retirement quality of life.

In this study, we focus on an important but previously unexplored determinant of the stock

investment decisions of older investors, namely, cognitive aging. We examine whether older

people make better investment choices as they gain more investment knowledge and experience,

or whether their investment skill deteriorates with age due to the adverse effects of cognitive

aging. This is an important issue that has implications for how individual investors should

structure their portfolios over time, the type of investment advice they should seek over their

lifetime, and the potential effects of changes in government policy on investment generated

retirement income. To our knowledge, this is the first study that highlights the potential role

and the importance of cognitive aging in people’s investment decisions.

The extant evidence from cognitive aging and learning research indicates that aging and

learning processes operate jointly. In particular, studies in cognitive aging demonstrate that

both physical and cognitive abilities, especially memory, decline with age (e.g., Horn (1968), Fair

(1994, 2004), Salthouse (2000), Schroeder and Salthouse (2004)). Further, research in learning

suggests that with experience, older investors might accumulate greater investment knowledge

and exhibit greater awareness of the fundamental principles of investing. Their accumulated

investing wisdom could help them make better investment decisions. Investors might also be

less prone to behavioral biases as they grow older and become more experienced (e.g., List

(2003), Feng and Seasholes (2005), Dhar and Zhu (2006), Goetzmann and Kumar (2008)).

Motivated by these earlier findings, we conjecture that, on the one hand, older investors

would accumulate greater knowledge about the fundamental principles of investing. But on the

other hand, their declining cognitive abilities would hinder the effective application of those

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principles. If the adverse effects of aging dominate the positive effects of experience, older

investors’ portfolios would under-perform common performance benchmarks. Using the end-of-

month portfolio holdings and trades of a sample of individual investors at a large U.S. brokerage

house, we empirically test this dual pronged conjecture.

The empirical analysis focuses on the relative influences of age and investment experience on

investors’ portfolio decisions and performance. We estimate “rules of thumb” and “skill” regres-

sions, where the dependent variable is either a measure that reflects the outcome of following

an investment rule of thumb or a measure of investment skill. The key explanatory variables

are age and investment experience. We use age to capture the adverse effects of cognitive aging

and use experience (the number of days between the account opening date and December 31,

1996) to capture the positive effects of experience.2 Without the experience measure, age would

capture two confounding effects, one related to experience and the other related to cognitive

aging. By including age and experience variables simultaneously, we attempt to separate the

positive effects of experience from the negative effects of cognitive aging.

Our empirical evidence strongly supports our main conjecture. Consistent with the theo-

retical predictions of life-cycle and learning models, we find that older and more experienced

investors hold less risky portfolios, exhibit stronger preference for diversification, trade less fre-

quently, exhibit greater propensity for year-end tax-loss selling, and exhibit weaker behavioral

biases. And consistent with the psychological evidence, we find that older investors exhibit

worse stock selection ability and poor diversification skill. The age-skill relation has an inverted

U-shape and, furthermore, the skill deteriorates sharply around the age of 70. These results

suggest that older investors exhibit a greater propensity to use common investment rules of

thumb but they appear less skillful in successfully implementing those rules.3

To gather additional support for our main hypothesis, we seek guidance from the psychol-

ogy literature that examines the conditional effects of cognitive aging. The evidence from this

literature indicates that people who are more educated, more resourceful, and undertake intel-

lectually stimulating jobs are able to better compensate for their declining cognitive abilities

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(Arbuckle, Gold, and Andres (1986), Baltes and Lang (1997), Cagney and Lauderdale (2002)).

The evidence also suggests that the age-related decline in cognitive abilities is steeper for African

Americans and Hispanic minority groups (e.g., Avolio and Waldman (1986), Black (2004)).

Motivated by these findings in cognitive psychology, we use age-income, age-education, age-

race, and age-ethnicity interaction terms as additional proxies for cognitive aging and examine

the conditional deterioration in cognitive abilities with age. Consistent with our hypothesis, we

find that the adverse effects of aging are stronger among older investors who are also relatively

less educated, earn lower income, and belong to the Hispanic ethnic group.

Because we cannot measure the adverse effects of cognitive aging directly, our results are

open to alternative interpretations. To further ensure that the variables we use to capture

cognitive aging are appropriate, we estimate a model of cognitive aging using a representative

European household-level data set, which includes direct measures of cognitive abilities. The

model estimates indicate that cognitive abilities increase with education, wealth, and income

but decline with age. There is a sharp decline after the age 70 and, moreover, the cognitive

decline is steeper among older individuals who are also less educated and have lower income.

These results indicate that demographic variables such as age, income, wealth, education, and

their interactions are likely to capture the adverse effects of cognitive aging reasonably well.

Studies like ours that examine the effects of age also face the classic age-cohort-period iden-

tification problem (e.g., Deaton (1997), Ameriks and Zeldes (2004)). A potential alternative

interpretation of our evidence on cognitive aging is that it reflects birth cohort effects. While

plausible, there are several reasons why cohort effects are unlikely to explain our main findings.

First, it is difficult to conceive a hypothesis based on cohort effects that predicts the observed

opposite effects of age in our rules of thumb and skill regressions. Put differently, cohort effects

cannot easily explain why older investors would exhibit a greater propensity to follow common

investment principles but exhibit a lower ability to apply them effectively. Second, cohort-based

explanations for the observed sudden drop in performance at older age are unlikely to be con-

vincing. Third, cohort effects cannot successfully account for the inverted U-shaped relation

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between age and investment skill. Last, the performance differential between younger and older

investors increase with portfolio size, which we interpret as a proxy for task difficulty. There is

no obvious cohort-based explanation for this result. In contrast, all these findings are strongly

consistent with the cognitive aging hypothesis and reflect the natural outcome of the joint aging

and learning processes.

To further account for the effects of birth cohorts, we perform an individual-level comparison

and use the differencing method proposed in McKenzie (2006). For each investor, we compute

the change in performance between the first and the second halves of the sample period and

examine whether the performance differential varies with age. By differencing, we eliminate

the common effects associated with cohorts. We find that the performance differential measure

exhibits an inverted U-shaped pattern and, similar to the age-skill relation, there is a sharp

decline at very old age. This evidence is consistent with the cognitive aging hypothesis and does

not suffer from potential contamination from cohort effects.

Examining the economic costs of aging, we find that, on average, investors with stronger

aging effects earn about 3% lower risk-adjusted annual returns, and the performance differential

is over 5% among older investors with large portfolios. These performance differentials remain

economically significant even when we account transaction costs and use net returns to measure

performance. We conduct several robustness tests and show that our results are not sensitive

to the relatively short sample size, exceptional performance of certain styles and industries, the

choice of skill measures, potential error in skill measurement, our inability to observe investors’

full portfolios, choice of the risk adjustment methodology, specific market conditions, investors’

lack of interest in relatively small portfolios, and the geographical concentration of our sample

investors.

At a first glance, these empirical findings might appear puzzling, and perhaps surprising,

because the finance literature on portfolio choice mainly attributes increasing risk aversion and

the positive effects of experience to the aging process. The adverse effects of cognitive aging are

typically ignored. Within this traditional portfolio choice paradigm, it is very difficult to conceive

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a hypothesis that posits a positive impact of experience and the negative impacts of age, age-

income, age-education, and age-race/ethnicity interaction terms on investment skill. However,

when interpreted in the appropriate context of the extant psychological evidence on cognitive

aging, our findings appear intuitive and economically meaningful because they represent the

natural outcome of the joint aging and learning processes.

The rest of the paper is organized as follows. In the next section, we develop the main

testable hypotheses. We describe the data in Section III and, in Section IV, we test our first

hypothesis that focuses on the positive effects of aging and experience. In Section V, we test our

unconditional and conditional hypotheses, which posit that stock investment skill deteriorates

with age but improves with experience. In Section VI, we estimate the economic costs of aging.

In Section VII, we conduct robustness checks and attempt to rule out alternative interpretations

of our key findings. We conclude in Section VIII with a brief summary of the paper and potential

implications of our results.

II. Hypothesis Development and Related Research

We develop our testable hypotheses by synthesizing the empirical evidence from the psychological

research on aging, the literature on learning, and life-cycle models of investing. The extant

psychological evidence indicates that the decline in cognitive abilities is a normal consequence

of biological aging and this phenomenon is observed across different countries and cultures (Craik

and Salthouse (1992)).

Both physical and cognitive abilities, especially memory, decline with age (e.g., Horn (1968),

Fair (1994, 2004), Salthouse (2000), Schroeder and Salthouse (2004)), where the decline begins

at a relatively young age of 30 (Grady and Craik (2000)). Weakening memory slows down the

information processing ability of individuals and leads to a decline in older people’s ability to

perceive conditional probabilities (Spaniol and Bayen (2005)). In addition, due to a decline

in attentional ability, older people get distracted easily and are unable to distinguish between

6

relevant and irrelevant information. Overall, the evidence suggests that older people would

react to new information inappropriately because they are typically slower and less effective at

processing and integrating new information.

The psychological evidence also indicates that people are likely to experience a decline in

the level of their general intelligence as they grow older. The aging process influences general

intelligence through two distinct channels. First, general intelligence declines with age due to the

adverse effects of aging on memory and attention (e.g., Lindenberger and Baltes (1994), Baltes

and Lindenberger (1997)). Second, the sensory (vision and hearing) functioning worsens with

age and is associated with lower levels of intelligence. The decline in intelligence is much steeper

after the age of 70 (Lindenberger and Baltes (1997)), while these adverse effects are attenuated

in people’s area of expertise due to frequent practicing (Masunaga and Horn (2001)).

In addition to biological and psychological factors, socioeconomic and demographic factors

such as education, income, wealth, race, ethnicity, and gender can exacerbate the adverse effects

of cognitive aging. For example, people who are more educated, more resourceful (i.e., have

higher income and are wealthier), and undertake intellectually stimulating jobs experience a

slower decline in cognitive abilities because they are able to actively compensate for the adverse

effects of aging (Arbuckle, Gold, and Andres (1986), Baltes and Lang (1997), Cagney and

Lauderdale (2002)). In contrast, the age-related decline in cognitive abilities is steeper among

older women (Shanan and Sagiv (1982)) as well as older African Americans and Hispanics

(Avolio and Waldman (1986), Black (2004)).

While old age is likely to have an adverse effect on people’s ability to make effective in-

vestment decisions, older investors are likely to have greater investment experience and greater

awareness of the fundamental principles of investing. Their accumulated investing wisdom could

help them make more efficient investment decisions. Theoretical models of portfolio choice (e.g.,

Bakshi and Chen (1994), Campbell and Viceira (2002), Cocco, Gomes, and Maenhout (2005),

Gomes and Michaelides (2005)) also posit that the riskiness of investor portfolios would decline

with age due to decreasing investment horizon and increasing risk aversion.4

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In addition to these channels, investors are likely to learn through the process of trading,

and they might be less prone to behavioral biases as they grow older and become more experi-

enced. The extant empirical evidence from the individual investor literature indicates that older

investors exhibit a weaker disposition effect (Dhar and Zhu (2006)), hold less concentrated port-

folios (Goetzmann and Kumar (2008)), and exhibit lower degree of over-confidence (Barber and

Odean (2001)). Furthermore, these behavioral biases decline as investors learn and gain more

experience (e.g., List (2003), Feng and Seasholes (2005), Goetzmann and Kumar (2008)). Older

investors are also less prone to gambling type activities in the stock market (Kumar (2009)).

Overall, the consensus that emerges from cognitive aging and learning research suggests that,

on the one hand, older investors are likely to make relatively more conservative choices and might

possess relatively greater knowledge about the fundamental principles of investing. But on the

other hand, effective application of those principles requires efficient processing of information,

which they might lack.5 Given the opposite predictions of aging and learning research, our paper

investigates empirically whether declining cognitive abilities or increasing investment experience

has a stronger influence on investors’ stock investment decisions.

We test three hypotheses. First, based on the evidence from learning studies, we posit that:

H1: Investment knowledge increases with both age and experience.

Next, based on the extant psychological evidence, we develop our unconditional hypothesis,

which posits that:

H2: Investment skill increases with experience due to the positive effects of learning

but declines with age due to the adverse effects of cognitive aging.

While support for the unconditional hypothesis would provide evidence consistent with the

predictions of cognitive aging, in the absence of a direct measure of cognitive aging, the following

conditional hypothesis would strongly reinforce that evidence:

H2cond: The decline in investment skill is steeper among older investors who are

less educated, earn lower income, and belong to a racial/ethnic minority group.

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In the following sections, we test these hypotheses using data from multiple sources.

III. Data and Sample Selection

The main data set for this study consists of all trades and end-of-month portfolio positions of

investors at a major U.S. discount brokerage house for the 1991 to 1996 time period. There are

77,995 households in the retail database who hold common stocks and trade a variety of other

securities including mutual funds, options, American depository receipts (ADRs), etc. In this

study, we focus on the investment behavior of 62,387 investors who have traded common stocks.

For a subset of households, demographic information such as age, income, wealth, occupation,

marital status, gender, etc. is available. The demographic measures such as age, income, marital

status, family size, etc. were compiled by Infobase Inc. a few months after the end of the sample

period (June 1997). The total wealth is reported at the account opening date.6

An average investor holds a four-stock portfolio (median is three) with an average size of

$35,629 (median is $13,869). The average aggregate value of investor portfolios in our sample

is about 2.18 billion and our sample investors executed about 1.9 million common stock trades

during the six-year sample period. Investors’ stock holdings and trades encompass about 90% of

stocks (9,011 stocks) from the Center for Research on Security Prices (CRSP) universe. Further

details on the investor database are available in Barber and Odean (2000).

Table I, Panel A reports summary statistics for five groups of investors grouped as age

cohorts. Because our primary focus is on the investment behavior of older investors, in Panel

B, we also provide summary statistics for five groups of older investors (age ≥ 60) grouped

as age cohorts. A typical investor in our sample has held a brokerage account for about ten

years, and as expected, investment experience increases with age. More importantly, we find

that consistent with the prior evidence (e.g., Poterba (2001)), the mean portfolio size increases

monotonically with age and there is no evidence that older investors reduce their exposure to

equity as their investment horizon decreases. In fact, older investors have greater proportional

9

investment in the stock market, both when measured as a proportion of their total wealth and

their annual income.

The cross-sectional variations in wealth and income in our sample also match well with

corresponding cross-sectional variations in the more representative Survey of Consumer Finances

(SCF) data. For instance, consistent with the evidence in Poterba (2001), we find that the wealth

level peaks within the age range of 65-69. Additionally, we find that the annual income peaks

within the age range of 47-52, which is also consistent with the predictions of the life-cycle

models. These comparisons with the SCF data suggest that our sample of older retail investors

is reasonably representative of the older households in the U.S.7

To enrich our analysis, we complement the individual investor data with demographic data

from the 1990 U.S. Census. We use the Census data to identify the racial/ethnic profile and

the educational background of investors. To identify the racial/ethnic composition of investors,

for each zip code, we compute the proportion of individuals in the following four racial/ethnic

groups: (i) Caucasian, (ii) African American, (iii) Hispanic, and (iv) Others. Using the zip code

of each investor, we assign her the appropriate zip code-level racial/ethnic profile. Similarly,

we use the Census data to infer the education level of an investor. Investors who live in more

educated zip codes are assumed to be more educated, where the proportion of the zip code

population that holds a bachelor’s or higher degree is used to identify the educational status of

that zip code.

Several other data sets are used in this study. We use a representative household-level data

set from the 2005 wave of the Survey of Health, Aging, and Retirement in Europe (SHARE) to

estimate a model of cognitive abilities. We use data from the 2005 Dutch DNB Household Survey

for some of our robustness checks. For each stock in the sample, we obtain the quarterly cash

dividend payments, monthly prices, returns, and market capitalization data from the Center

for Research on Security Prices (CRSP) and quarterly book value of common equity data from

COMPUSTAT. We obtain the monthly time-series of the three Fama-French factors and the

momentum factor from Professor Kenneth French’s data library. Last, we obtain characteristic-

10

based performance benchmarks from Professor Russ Wermer’s web site.8

IV. Age, Experience, and Investment Knowledge

In this section, we gather support for our first main hypothesis (H1). Specifically, we examine

whether the knowledge and experience accumulated over time are reflected in investors’ portfolio

holdings and trading decisions.

A. Age and Equity Portfolio Risk

In our first formal test, we investigate whether older investors tilt their portfolios toward rel-

atively less risky stocks. We estimate panel regression models to examine the characteristics

of age based group portfolios in a multivariate setting. In these regressions, the excess weight

assigned to a stock in the aggregate group portfolio is the dependent variable and the mean

return, idiosyncratic volatility, skewness, kurtosis, and the price of the stock are used as the

primary independent variables.9 The group portfolio is constructed by combining the portfolios

of all investors who belong to the group. The return moments are calculated using the past 60

months of data and the idiosyncratic volatility measure is the variance of the residual obtained

by fitting a four-factor model to the monthly stock returns series. Additionally, we consider the

following control variables to characterize investors’ stock preferences: (i) market beta, which is

also estimated using past 60 months of data, (ii) firm size, (iii) book-to-market ratio, (iv) short-

term momentum (past one-month stock return), (v) longer-term momentum (past twelve-month

stock return), (vi) an S&P500 dummy that is set to one if the stock belongs to the S&P500

index, (vii) monthly volume turnover, and (viii) annual dividend yield.

We account for potential auto-correlation and cross-correlation in errors using the non-

parametric approach of Driscoll and Kraay (1998) and obtain the corrected standard errors

for our estimates. This methodology provides a unified approach for simultaneously correcting

the standard errors for cross-sectional correlation, serial correlation, and cross serial correlation

11

in a panel setup. To ensure that extreme values are not affecting our results, we winsorize all

variables at their 0.5 and 99.5 percentile levels. Further, to facilitate comparisons among the

coefficient estimates, the independent variables are standardized so that each variable has a

mean of zero and a standard deviation of one.

The panel regression estimates are presented in Table II. We estimate the panel regression

model for three age-based categories: (i) younger age group containing investors in the 20-38

age range, (ii) older age group consisting of investors in the 60-94 age range, and finally, (iii)

within the older investor group, the oldest age group consisting of investors in the 75-94 age

range. Additionally, we estimate two panel regressions to examine the differences in the stock

preferences of groups (i) and (ii), and (i) and (iii).

Focusing on the differential regression estimates (see columns (4) and (5)), we find that older

investors favor relatively less risky stocks. Specifically, older investors’ preferences for stocks with

higher idiosyncratic volatility, higher market beta, lower market capitalization, lower prices are

weaker than those of younger investors. In addition, older investors exhibit weaker preference

for stocks with higher skewness, which indicates they are less likely to chase extreme positive

returns. Our estimates also indicate that investors’ preferences for less risky stocks increase with

age. The differences in the stock preferences of younger and older investors, as reflected by the

magnitudes of the coefficient estimates, are stronger when we consider the 75-94 age group to

identify older investors (see column (5)).10

Collectively, the panel regression estimates indicate that the average risk exposures of in-

vestors’ stock portfolios decrease with age. Consistent with our first hypothesis (H1), the ev-

idence indicates that experienced and prudent investors reduce the riskiness of their portfolios

as they grow older.

B. Do Investors Accumulate More Knowledge As They Grow Older?

To examine whether older investors possess greater knowledge about investing, we concentrate

on several important dimensions of portfolio decisions that reflect common investment “rules

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of thumb”. The set of decisions that we consider is guided by the availability of data. First,

we examine whether older investors are more likely to recognize the potential benefits of diver-

sification. Next, we examine whether older investors trade less frequently because they realize

that they would not be able to improve performance through active trading. Last, we examine

whether older investors are more likely to engage in year-end tax-loss selling, since it requires

financial awareness but does not necessarily require skill.11

We estimate several rule of thumb cross-sectional regressions, where the dependent variable

is a measure of investment decision that reflects a specific investing rule of thumb. The measures

are obtained for each investor using their decisions during the entire sample period. For each

investment decision, we estimate both unconditional and conditional regression models. In the

unconditional regressions, the independent variables are only age and investment experience.

Age corresponds to the head of the household and Investment Experience is the number of days

between the account opening date and December 31, 1996.

In the conditional regressions, the following demographic variables and portfolio charac-

teristics are employed as control variables: Income represents the annual household income;

Education represents the proportion of people in investor’s zip code that has attained a bach-

elor’s or higher educational degree; Male Dummy is set to one if the head of the household

is male; Retired dummy is set to one if the head of the household is retired; Portfolio Size is

the average market capitalization of the household portfolio; Portfolio Turnover is the average

of monthly buy and sell turnovers; and Portfolio Dividend Yield is the average dividend yield

of the household portfolio. The RMRF (market factor), SMB (small-minus-big factor), HML

(high-minus-low factor), and UMD (up-minus-down or momentum factor) exposures are the

factor loadings of an investor’s portfolio and characterize the riskiness of the portfolio. The

factor loadings are obtained by fitting a four-factor time-series model to the monthly portfolio

return series of each investor for the period in which the investor is active. Last, Mutual Fund

Holdings is the proportion of the equity portfolio that is allocated to mutual funds.

The rule of thumb cross-sectional regression estimates are presented in Table III, where the

13

t-statistics are computed using robust and zip code-level clustered standard errors. As before,

we winsorize all variables at their 0.5 and 99.5 percentile levels and the independent variables

are standardized. In the first two regressions, we use the number of stocks in the portfolio as the

dependent variable to examine whether older investors are more aware of the potential benefits

of diversification (columns (1) and (2)). Our intent here is not to show that older investors hold

more diversified stock portfolios. Given that we cannot observe the entire portfolios of investors,

the number of stocks is likely to be a very noisy measure of diversification. Nonetheless, the

number of stocks in an investor’s equity portfolio is likely to indicate whether or not an investor

exhibits a preference for diversification and at least attempts to diversify.12

Our results from the unconditional model indicate that older and more experienced investors

hold portfolios containing a greater number of stocks. The coefficient estimates are significantly

positive for both Age and Investment Experience, even in the presence of various control vari-

ables. The coefficient estimates for the control variables are also broadly consistent with our

expectations. For instance, the positive coefficient estimate for Mutual Fund Holdings indicates

that investors who exhibit stronger preference for diversification in their stock portfolios also

hold more mutual funds. Overall, consistent with our first hypothesis, the evidence indicates

that the portfolio choices of older and more experienced investors are more likely to conform to

one of the key principles of investing, namely, portfolio diversification.

Next, we examine whether older investors follow one of the key recommendations of the effi-

cient market hypothesis, which posits that investors cannot improve performance through active

trading. In the next two regression specifications (columns (3) and (4)), we use the monthly

portfolio turnover as the dependent variable.13 Again, consistent with our first hypothesis, we

find that both older and more experienced investors exhibit lower turnover rates. The coefficient

estimates are significantly negative for both Age and Investment Experience, even in the presence

of various control variables. The negative coefficient estimate for Age and the positive coefficient

estimate for the Male Dummy are consistent with the evidence in Barber and Odean (2001),

who find that older (male) investors trade relatively less (more) frequently. These estimates

14

indicate that the trading behavior of older investors are more likely to conform to another key

principle of investing, namely, less frequent trading.

While these cross-sectional regression estimates are consistent with our first hypothesis, one

might conjecture that a stronger preference for diversification and lower portfolio turnover do not

necessarily imply greater investment knowledge but merely reflect “passive” investing by older

investors. For example, an older investor might hold more stocks in her portfolio not because

she has a preference for diversification, but because she has accumulated a large number stocks

during a long investing period. To address this potential concern, we use a knowledge measure

that is more likely to capture investor’s knowledge about investing. Specifically, we examine

whether older investors exhibit a greater propensity to engage in year-end tax-loss selling.

We estimate a regression model in which the proportion of “losers” (stock investments in

which an investor suffers a loss) sold in the month of December is used as a dependent variable.

The regression estimates indicate that both older and more experienced investors are more will-

ing to sell their losers in December (see column (5)). The coefficient estimates are significantly

positive for both Age (estimate = 0.016, t-stat = 5.696) and Investment Experience (estimate

= 0.006, t-stat = 2.311), even in the presence of various control variables. Again, we find that

most control variables have the expected signs. For instance, investors who hold larger portfolios

and trade more often are likely to sell more losers in December. This evidence indicates that

the trading behavior of older investors reflect yet another investing rule of thumb: “Sell your

losers in December”.

Given that the coefficient estimates of Age and Investment Experience have similar signs in

all cross-sectional regression specifications, one might suspect that the two variables capture

identical aspects of investors’ investment decisions. But we find that age and investment expe-

rience measures are weakly correlated (correlation = 0.142). Furthermore, when we estimate a

cross-sectional regression with portfolio dividend yield as the dependent variable, we find that

the coefficient estimate for Age is positive but the coefficient estimate for Investment Experience

is negative (see column (6)). The positive coefficient estimate for Age is consistent with the

15

evidence in Graham and Kumar (2006), who show that older investors are likely to prefer high

yield stocks for consumption reasons. However, the negative estimate for Investment Experience

is new and it indicates that, all else equal, more experienced investors prefer lower yield stocks.

In the current context, more importantly, the estimates indicate that the age and experience

variables capture two distinct aspects of investors’ portfolio choices and trading decisions.

C. Other “Rules of Thumb”

While it is very difficult to perform a comprehensive analysis of rules of thumb recommended

by investment advisors, we study whether older and experienced investors exhibit a greater

propensity to follow other commonly prescribed rules of thumb. The results from these addi-

tional empirical tests are summarized in Table III, Panel B. First, we examine whether older

investors exhibit a higher propensity to spread their positions across multiple asset classes. We

also investigate whether older investors are more likely to diversify using low expense mutual

funds and foreign stocks.

Consistent with the evidence on diversification preference, the estimates from test (1) show

that both older and experienced investors invest in a greater number of asset classes. We also find

that both older and experienced investors hold mutual funds with lower expense ratios and hold a

larger proportion of foreign stocks in their equity portfolios (see tests (2) and (3)).14 For example,

the expense ratio differential between a 30 year old and a 65 year old investor is 0.078%, which

is about 9.10% higher than the mean expense ratio of sample investors (= 0.857%). Similarly,

older investors allocate 2.02% more weight to foreign stocks than younger investors. This is more

than 50% higher than the sample mean foreign stock weight of 3.87%. These results indicate

that older investors are more likely to follow two other common investment rules of thumb:

“Invest in well-diversified, low expense mutual funds” and “Diversify internationally.”15

Next, in tests (4) and (5), we examine whether both older and experienced investors exhibit

weaker behavioral biases such as the disposition effect and local or familiarity bias. We find that

consistent with the greater investment knowledge hypothesis, older and experienced investors

16

are less likely to hold on to their losers (i.e., they exhibit a weaker disposition effect) and exhibit

a relatively lower propensity to hold local stocks (i.e., exhibit a weaker local bias).16

Last, we examine whether older investors shy away from relatively sophisticated trading

strategies such as margin trading, short selling, and option trading (see tests (6) to (8)). We

find that older investors are less likely to hold a short position or trade options. In contrast,

experienced investors are more likely to hold short positions and they also exhibit a greater

propensity to trade options. Investors with greater experience are also more likely to have a

margin trading account. These findings suggest that experience might be a proxy for financial

sophistication and could be positively correlated with investment skill.

D. Evidence From the Dutch DNB Data

To further examine the robustness of our rules of thumb regression results, we consider data

from another country. We use the Dutch DNB data and examine whether older and experienced

investors exhibit stronger diversification motives. The DNB data contain information about the

aggregate holdings in stocks, bonds, and mutual funds but do not provide information about the

types of assets investors hold or trade. We also have information about the respondent’s age, in-

come, education, gender, self-reported knowledge of financial markets (our proxy for investment

experience), self-reported cognitive ability measures, and other demographic variables.

Using the mutual fund participation dummy as a proxy for the intent to diversify, we estimate

a logit model, where the mutual fund participation dummy is the dependent variable and the

various demographic variables including age, experience, and cognitive ability are the indepen-

dent variables.17 The results are reported in Table III, Panel C. Consistent with the results from

the U.S. brokerage data, we find that older and more knowledgeable Dutch investors exhibit a

higher probability of holding mutual funds (see test (1)). The results are similar when we use an

alternative measure to capture investors’ diversification motives: an “All Asset Classes” dummy

that is set to one if an investor holds stocks, bonds, and mutual funds. We find that both Age

and Experience have significantly positive coefficient estimates (see test (2)).

17

When we include the cognitive ability index as an additional dependent variable, in unt-

abulated results, we find that higher levels of cognitive ability increase the mutual fund par-

ticipation probability (estimate = 0.321, z-stat = 2.225). High cognitive ability investors also

exhibit a greater propensity to invest in all asset classes, although the coefficient estimate is

only marginally significant (estimate = 0.577, z-stat = 1.671). These results indicate that like

cognitive abilities, age and experience are positively correlated with investment knowledge.

Overall, our rule of thumb cross-sectional regression results indicate that older investors

make more conservative stock investment choices and their choices reflect greater knowledge

about investing. This evidence supports our first hypothesis (H1), which posits that investment

knowledge increases with both age and experience. Furthermore, the evidence indicates that

investors with greater experience appear more sophisticated and could be skilled.

V. Cognitive Aging and Investment Skill

While older investors, especially those who are more experienced, exhibit a greater propensity

to follow common investment rules of thumb, how effectively can they apply those principles? In

this section, we examine the relation between age, investment experience, and investment skill

and gather support for our second set of hypotheses (H2 and H2cond), which posit opposite

effects of age and experience on investment skill.

A. Graphical Evidence: Univariate Results

Figure 1 shows the univariate relation between age and investment skill, as captured by the

Daniel, Grinblatt, Titman, and Wermers (1997) characteristic-adjusted performance measure.

Two features of the plot are noteworthy. First, the investment performance exhibits an inverted

U-shape with a peak at around 42 years. The hump shape reflects the combined effects of

experience and aging. This evidence is consistent with the findings in Agarwal, Driscoll, Gabaix,

and Laibson (2007), who find a similar pattern in the borrowing rates of households in various

18

credit markets. Second, there is an abrupt and significant drop in investment performance

around the age of 70. This nonlinear effect supports our cognitive aging hypothesis and is

consistent with the evidence from studies in psychology that document a steeper cognitive

decline after the age of 70. Overall, the graphical evidence reveals that the interactions between

the aging and learning processes determine the risk-adjusted performance of investor portfolios.

B. Opposite Effects of Age and Experience

We attempt to uncover these interactions by estimating “skill” regressions. In these cross-

sectional regressions, a measure of investment skill is employed as the dependent variable. We

focus on two specific investment skill measures: the “diversification skill” and the stock selec-

tion ability. Our conjecture is that although older investors hold portfolios with larger number

of stocks, they might not possess “diversification skill” because the ability to perceive corre-

lations accurately would decline with age.18 Furthermore, investors’ stock selection skill could

decline with age because the adverse effects of cognitive aging would influence people’s ability

to efficiently process new information. In contrast, both diversification skill and stock selection

abilities would improve with investment experience.

We use the monthly Sharpe ratio to measure diversification skill and the monthly portfolio

alpha to measure stock selection skill. For each investor, the realized portfolio return series

during the full sample period is used to compute the two performance measures. The Sharpe

ratio measure is defined as SRp = (µp−rf)/σp, where µp is the average realized portfolio return,

σp is the standard deviation of the portfolio return series, and rf is the risk-free rate of return.

The alpha measure is the intercept obtained by fitting a four-factor time-series model to the

portfolio return series. The factor model includes the market (RMRF), size (SMB), value (HML),

and momentum (UMD) factors. We also employ the mean characteristic-adjusted monthly

portfolio return measure computed using the Daniel, Grinblatt, Titman, and Wermers (1997)

methodology as an alternative measure of investment skill.19 Both investment skill measures

capture the ability of investors to generate excess returns from their portfolio decisions, after

19

accounting for the known differences in their stock preferences (see Table II).

In the first set of skill regressions, we test our unconditional hypothesis. The only inde-

pendent variables in these regression specifications are Age and Investment Experience. The

cross-sectional regression estimates for the unconditional models are presented in Table IV,

Panel A (columns (1), (3), and (5)). In all our regression specifications, we use robust, clustered

standard errors to account for potential cross-sectional dependence in performance within zip

codes.

In the Sharpe ratio regression (column (1)), Age has a negative but statistically insignificant

coefficient estimate (estimate = −0.001, t-stat = −0.935), while Investment Experience has

a significantly positive coefficient estimate (estimate = 0.011, t-stat = 11.644).20 In the alpha

regression (column (3)), Age has a significantly negative coefficient estimate (estimate = −0.042,

t-stat = −5.047) and Investment Experience has a positive but statistically insignificant estimate

(estimate = 0.010, t-stat = 1.184). Last, in the characteristic-adjusted return regression (column

(5)), Age has a significantly negative coefficient estimate (estimate = −0.044, t-stat = −7.293)

while Investment Experience has a significantly positive coefficient estimate (estimate = 0.037, t-

stat = 6.053). These coefficient estimates are broadly consistent with our second main hypothesis

and indicate that Age has opposite effects in rule of thumb and skill regressions.

The coefficient estimates in the skill regressions are also significant in economic terms. For

instance, the estimate for Age in the alpha regression indicates that, holding experience fixed,

a one standard deviation shift in the age of an investor would correspond to an annual, risk-

adjusted performance decline of 0.042 × 12 = 0.504%. The mean age of investors in our sample

is 50 and the standard deviation is about 12. Thus, when an investor aged 30 becomes older

and crosses the retirement age of 65 (a three standard deviation change in age), she is likely to

suffer an annual performance decline of 1.512% on a risk-adjusted basis.

Collectively, the graphical evidence and the results from our unconditional tests indicate

that, investment skill varies inversely with age and positively with investment experience. This

evidence is consistent with our unconditional hypothesis (H2), although the strengths of age-skill

20

and experience-skill relations are not very strong.21

C. Model of Cognitive Abilities and Skill Regression Specification

We consider additional proxies for cognitive aging to gather stronger support for the second

hypothesis. Our choice is motivated by previous studies in cognitive psychology, which demon-

strate that individuals who are more educated, more resourceful, and undertake intellectually

stimulating jobs are able to better compensate for their declining cognitive abilities (Arbuckle,

Gold, and Andres (1986), Baltes and Lang (1997), Cagney and Lauderdale (2002)). Analogous

to the psychological evidence, we expect that the adverse effects of cognitive aging would be

weaker among wealthier, higher income, and more educated investors. Older investors who are

more educated and more resourceful (i.e., have higher income levels and are wealthier) might

be able to better compensate for their declining information processing abilities.

To ensure that the additional cognitive aging proxies employed in the skill regression specifi-

cation are appropriate, we estimate a model of cognitive abilities using a representative European

household data set and show that our cognitive aging proxies are strongly correlated with direct

measures of cognitive abilities. We choose the European data set because it contains three direct

measures of cognitive abilities: (i) verbal ability, (ii) quantitative ability, and (iii) memory. The

three cognitive measures are positively correlated but the maximum correlation is below 0.50.

Using these measures, we obtain a composite (equal-weighted) measure of cognitive abilities.

The European household data also contain demographic variables that are available in our in-

dividual investor data set. We consider several regression specifications, where one of direct

measures of cognitive abilities is the dependent variable and the main determinants of cognitive

abilities identified in the psychology literature are the independent variables.

The cognitive abilities regression estimates are reported in Table V. Consistent with the

evidence from psychology, we find that cognitive abilities decline with age and are positively

associated with education, wealth, and income. Furthermore, the decline is steeper among

individuals who are considerably older (age > 70), are less educated, and have lower income. It

is interesting that two facets of cognitive abilities that are more relevant for investment decisions,

21

namely, the quantitative ability and memory, exhibit a sharper decline with age. The decline

in verbal ability that might be less relevant for investment decisions is relatively less severe.

Collectively, the cognitive abilities model estimates indicate that demographic variables such as

age, income, wealth, education, and their interactions are likely to capture the adverse effects

of cognitive aging reasonably well.

Motivated by this evidence from our cognitive abilities model, we consider an extended skill

regression model with multiple cognitive aging proxies and attempt to capture the influence

of cognitive aging on investment decisions more accurately. Specifically, we interact age with

income and education, where both the Age×Low Income and Age×Low Education interaction

terms are defined after standardizing the age variable. We also consider an Over 70 Dummy to

capture the sudden drop in investment performance identified in Figure 1.

The evidence from research in cognitive psychology (e.g., Avolio and Waldman (1986), Black

(2004)) suggests that the age-related decline in cognitive abilities is steeper among ethnic/racial

minorities (African Americans and Hispanics). In light of this evidence, we use two additional

interaction terms, one for Hispanics and another for African-Americans. The Hispanic variable

is set to one for investors who live in zip codes where the ratio of the populations of Hispanics

to Whites is in the upper quintile. The African American variable is defined in an analogous

manner. We interact both race/ethnicity variables with Age.

Similar to the unconditional skill regressions, we consider several independent variables to

control for the known determinants of portfolio performance and investment skill. We include a

Male Dummy as a control variable because previous studies have shown that gender influences

net investment performance (Barber and Odean (2001)). The Retired Dummy allows us to

control for the significant lifestyle changes at the time of retirement, which could alter investment

behavior. We employ several portfolio characteristics as control variables because investors’ risk

preferences are likely to vary with age. This set includes portfolio size, portfolio dividend yield,

and the four factor exposures (RMRF , SMB, HML, and UMD coefficient estimates) of the

investor portfolio. Last, the Portfolio Turnover measure at least partially accounts for the effects

22

of transaction costs on portfolio performance.

D. Intent to Diversify versus Actual Diversification Skill

The diversification skill regression estimates for the conditional model is reported in Table

IV, Panel A, Column (2). Consistent with our second hypothesis, we find that the age-skill

and experience-skill relations become stronger and appear more transparent in the conditional

model. In the Sharpe ratio regression, both Age and Investment Experience have significant

coefficient estimates, where the loading on Age is negative (estimate = −0.014, t-stat = −3.355)

and the loading on Investment Experience is positive (estimate = 0.010, t-stat = 9.450). We

interpret the negative coefficient estimate on Age as the adverse effect of cognitive aging, while

the positive coefficient estimate on Investment Experience indicates that greater experience leads

to greater diversification skill.

Our results from the Sharpe ratio regression indicate that the coefficient estimate of Income

is positive but statistically insignificant. However, the Age×Low Income interaction term has

a negative coefficient estimate, which indicates that the adverse effects of aging are stronger

among older investors with lower income. In addition, we find that Education has a significantly

positive coefficient estimate (estimate = 0.002, t-stat = 1.882) and the Age×Low Education

interaction term has a marginally negative coefficient estimate. These results indicate that

while education and investment experience leads to more effective diversification, as investors

grow older, their ability to diversify effectively decreases.

Our results are similar when we use the average correlation among stocks in the portfolio

as an alternative measure of diversification skill. If investors diversify effectively, all else equal,

they would hold stocks that have lower correlations among them. When the average stock

correlation is the dependent variable in the skill regression, in untabulated results, we find

that Age has a significantly positive coefficient estimate (estimate = 0.006, t-stat = 3.032),

Investment Experience has a significantly negative coefficient estimate (estimate = −0.004, t-

stat = −3.903), and other coefficient estimates are very similar to the Sharpe ratio regression

23

estimates. This evidence indicates that although both older and experienced investors attempt

to diversify, only experienced investors demonstrate an ability to achieve effective diversification

and possess diversification skill.

We also obtain very similar results when we evaluate investors’ mutual fund choices. The

rules of thumb regressions in Section IV.C indicate that older investors are more likely to follow

the rule: “Invest in well-diversified, low expense mutual funds.” However, consistent with our

cognitive aging hypothesis, in untabulated results, we find that older investors do not earn higher

risk-adjusted returns from their increased participation rates in mutual funds. After accounting

for other factors, age is negatively related and experience is positively related to risk-adjusted

mutual fund performance. This evidence shows that in yet another setting older investors follow

the commonly prescribed investment principle but are relatively less effective in applying that

rule.22

The evidence from other related studies reinforce our diversification skill results. In particu-

lar, Bailey, Kumar, and Ng (2008) show that both older and experienced investors exhibit strong

intentions to diversify using foreign stocks, but only the experienced investors benefit from their

diversification attempts. This evidence indicates that older investors are more likely to attempt

to exploit the potential benefits of foreign investments but, conditional upon participation, they

appear less skillful in their decisions.

E. Conditional Deterioration in Stock Selection Abilities

When we estimate the conditional skill regression with the four-factor alpha as the dependent

variable (a measure of stock selection skill), the results are remarkably similar to the Sharpe

ratio regression estimates. These results are reported in Table IV, Panel A, Column (4). We

find that both Age and Investment Experience have significant coefficient estimates, where the

loading on Age is negative (estimate = −0.051, t-stat = −4.735) and the loadings on Investment

Experience and Education are positive (the estimates are 0.020 and 0.014, and the t-statistics

are 2.283 and 2.527, respectively). Further, the Over 70 Dummy has a negative and significant

24

coefficient estimate (estimate = −0.025, t-stat = −2.073). We also find that the Age×Low

Income and Age×Low Education interaction terms have negative coefficient estimates, though

the latter is not statistically significant.

When we use the mean characteristic-adjusted monthly portfolio return to measure risk-

adjusted performance, consistent with our alpha regression estimates, we find that age and

investment experience maintain their opposite signs and the interaction terms have similar

estimates (see column (6)).23 The coefficient estimate of Age is −0.054 with a t-statistic of

−2.945 and coefficient estimate of Investment Experience is 0.027 with a t-statistic of 3.891. In

addition, both Age×Low Income and Age×Low Education interaction terms have the expected

negative and significant coefficient estimates (the estimates are −0.014 and −0.005 with t-

statistics of −1.996 and −2.719, respectively).

While we use robust, clustered standard errors in our skill regressions to account for po-

tential cross-sectional dependence, for additional robustness, we estimate a panel regression

specification using the month-t characteristic-adjusted portfolio return as the dependent vari-

able. As before, we use the Driscoll and Kraay (1998) methodology to account for potential

cross-sectional correlation, serial correlation, and cross-serial correlation. We find that the panel

regression results reported in Column (7) are qualitatively very similar to the cross-sectional re-

gression estimates.

In untabulated results, we find that the coefficient estimates of our control variables have the

expected signs. For instance, in the alpha regression, the Portfolio Dividend Yield has a strongly

negative estimate, which indicates that investors who focus excessively on high dividend yield

stocks have weaker stock selection ability. Nonetheless, these investors are able to reduce the

total risk of their portfolios, thereby increasing the Sharpe ratio (see column (2)). Additionally,

investors who hold larger portfolios exhibit better stock selection ability because portfolio size

is likely to proxy for greater resources and it may also reflect greater investment experience.24

We also find that the coefficient estimate of Retired Dummy is statistically insignificant, which

suggests that the abrupt lifestyle change at the time of retirement does not have an incremental

25

negative effect on investment skill.

The coefficient estimates in the skill regressions are easy to interpret in economic terms.

They allow us to quantify the performance decline that can be attributed solely to the adverse

effects of cognitive aging. For instance, the coefficient estimate of Age in column (4) indicates

that, all else equal, a one standard deviation shift in the age of an investor who does not belong

either to the lower income, lower education, or ethnic minority groups would be associated

with an annual, risk-adjusted performance decline of 0.051 × 12 = 0.612%. This indicates that

when an investor aged 30 becomes older and crosses the retirement age of 65 (a three standard

deviation change in age), she is likely to suffer an annual performance decline of 1.836% on a

risk-adjusted basis.

Examining the race/ethnicity interactions, we find that Age×Hispanic interaction term has

a significantly negative coefficient estimate in all four regression specifications. For instance, in

the alpha regression, the coefficient estimate of the interaction term is −0.034, with a t-stat of

−3.516. In economic terms, this implies that an older investor who also earns lower income and

belongs to the Hispanic ethnic group would experience an annual, risk-adjusted performance

decline of (0.051 + 0.025 + 0.034) × 12 = 1.320%. For an investor with these attributes, a

jump in age from 30 to 65 would correspond to an annual performance decline of 3.960% on a

risk adjusted basis. In contrast, we find that the Age×African American interaction term has

insignificant coefficient estimates.

F. Stock Selection Skill Regression Estimates using Net Returns

Because older investors have lower turnover rates (see Section IV.B), their net performance after

accounting for transaction costs might not be significantly worse than younger investors. Using

the Barber and Odean (2000) method, we account for trading commissions, bid-ask spread, and

the potential market impact of investors’ trades and measure the net portfolio returns of each

investor portfolio. We re-estimate the skill regression using characteristic-adjusted net returns.

The results are reported in Column (8) of Table IV, Panel A.

26

Even when we use net portfolio return to measure skill, Age and Investment Experience

maintain their opposite signs and relative magnitudes. As expected, we find that the adverse

effects of aging are weaker when we use net returns but the performance decline that can be

attributed to aging remain economically significant. For instance, when an investor aged 30

becomes older and crosses the retirement age of 65 (a three standard deviation shift in age), she

is likely to suffer a net annual performance decline of 0.045 × 12 × 3 = 1.620%. If this investor

also earns lower income and belongs to the Hispanic ethnic group, she would experience a net

annual, risk-adjusted performance decline of (0.045 + 0.023 + 0.020) × 12 × 3 = 3.168%.25

Overall, the skill regression estimates support our unconditional hypothesis (H2), which

posits that investment skill increases with experience due to the positive effects of learning, but

declines with age due to the adverse effects of cognitive aging. The evidence also supports our

conditional hypothesis (H2cond), which posits that the decline in skill is steeper among less

educated and less wealthy older investors who belong to minority groups.

G. Cognitive Aging and Learning

Do older investors learn less effectively due to cognitive aging? To gather additional support

for our main hypothesis, we examine whether the speed and effectiveness of learning varies with

age. We embed two interaction variables in one of our skill regression specifications (column

(6) in Table IV, Panel A): Below 30×Low Experience and Over 70×Low Experience. In unt-

abulated results, we find that lack of experience has stronger adverse effects on older investors.

The coefficient estimate for the Over 70×Low Experience dummy is negative and significant

(estimate = −0.041, t-stat = −4.068) while the coefficient estimate of the Below 30×Low Expe-

rience dummy is statistically insignificant (estimate = 0.005, t-stat = 0.546). This evidence is

consistent with our conditional hypothesis and indicates that learning is impaired by the adverse

effects of cognitive aging.

27

H. Sub-Sample Estimates Without the Extreme Performers

While we have used multiple risk-adjusted performance measures to obtain “style adjusted”

portfolio performance, given our relatively short sample size, one might argue that the perfor-

mance differences reflect systematic age-induced style differences rather than the adverse effects

of cognitive aging. For instance, the style or industries (e.g., the technology sector) favored

by investors with higher cognitive abilities might have yielded exceptional returns during the

six-year sample period. Thus, it is possible that older investors do not have poor stock picking

skills but rather the styles chosen by them performed poorly during the sample period due to

chance.

To examine whether the exceptionally superior or poor performance of certain types of stocks

or industries are influencing our estimates, we exclude k% investors from both the top and the

bottom tails of the performance distribution and re-estimate the skill regressions. Even when

we choose k = 5, our estimates remain qualitatively similar to the baseline estimates reported

in Table IV, Panel A, Column (4). For instance, the untabulated results indicate that the

coefficient estimates for Age and Investment Experience are −0.047 (t-stat = −3.031) and 0.035

(t-stat = 4.609), respectively. Additionally, the interaction terms have the expected negative

and significant estimates.

I. Adverse Effects of Cognitive Aging or Cohort Effects?

Studies like ours that examine the effects of age are plagued with the classic age-cohort-period

identification problem (e.g., Deaton (1997), Ameriks and Zeldes (2004)). The main concern is

that in addition to age-induced cognitive aging effects that we are mainly interested in, age

could capture birth cohort or time effects. Because the three effects are strongly correlated, it

is usually difficult to isolate their effects without a data set that tracks the portfolio choices of

the same set of individuals over a very long period of time. Fortunately, time effects are unlikely

to play a significant role during the relatively short six-year sample period. Thus, we largely

assume that time effects are small and do not contaminate our results. We also find that our

28

main results hold for the 1991-93 and 1994-96 sub-samples (see Table VI), which indicates that

time-effects are not the primary drivers of our findings.

Focusing on cohort effects, we conjecture that there are several reasons why cohort effects

are unlikely to explain our findings. First, we use a combination of rules of thumb and skill

regressions to identify the adverse effects of cognitive aging, where our main hypothesis predicts

opposite effects of age in the two contexts. But just like the effects of experience, any cohort-

based hypothesis would predict a similar influence of age in both regressions. Common social

experiences such as the quality of education, socioeconomic environment when growing up, or

common first hand experience of salient events (e.g., the depression or the stock market crash)

that are often associated with cohort effects cannot successfully explain the opposite signs of age

in rules of thumb and skill regressions. Second, as shown in Figure 1, cohort-based explanations

for the abrupt and sudden drop in performance at older age are unlikely to be very convincing.

Third, cohort effects cannot successfully account for the inverted U-shaped relation between age

and investment skill. In contrast, all these findings are strongly consistent with the cognitive

aging hypothesis and reflect the natural outcome of the joint aging and learning processes.

Although our results so far seem inconsistent with cohort-based explanations, we conduct

several tests to directly account for the effects of birth cohorts. In the first test, we follow Poterba

and Samwick (1997) and define cohort-range dummy variables, where we consider five cohort

ranges: Below 35, 35-45, 45-55, 55-65, and above 65. In untabulated results, we find that the age-

range dummies have negative but insignificant coefficient estimates in all our specifications. More

importantly, the coefficient estimates of age, experience, and other interaction variables that

provide evidence in support of our main hypothesis remain significant. In fact, the coefficient

estimate of Age (see column (6) in Table IV, Panel A) becomes stronger (coefficient = −0.082,

t-stat = −3.129).

Next, we perform an individual-level performance comparison and find that the change in

performance between the first and the second halves of the sample period exhibits an inverted

U-shaped pattern (see Figure 1). The older investors experience a greater decline in performance

29

and similar to the age-skill relation, there is a sharp decline at very old age. This evidence is

consistent with the cognitive aging hypothesis and does not suffer from potential contamination

from cohort effects because differencing eliminates the common cohort effects (McKenzie (2006)).

The age-performance differential relation is qualitatively similar when we consider a multi-

variate estimation framework and account for other factors that might influence the sub-period

performance differential. Specifically, we estimate a cross-sectional regression in which the per-

formance differential between the two halves of the sample period is the dependent variable and

the set of independent variables includes the demographic characteristics used in the skill re-

gression. We find that Age and Investment Experience have opposite signs in the skill difference

regression (see Table IV, Panel A, column (9)). This evidence indicates that older investors

experience a decline in performance, while the performance of investors with greater experience

improves.

When we consider a quadratic age term to capture the hump shape of the age-performance

relation, we find qualitatively similar results. These results are reported in Panel B of Table

IV. When the dependent variable is one of the performance measures, both Age and Age2 have

negative and significant coefficient estimates (see columns (1) to (3)). This evidence indicates

that the inverted U-shape relation between age and investment skill is strong and significant

even when we account for other demographic factors and portfolio characteristics that may be

correlated with skill. When the dependent variable is the sub-period performance differential,

we again find that both Age and Age2 have negative and significant coefficient estimates (see

columns (4) and (5)). In both specifications, we also find that the Over 70 Dummy is signifi-

cantly negative, which is consistent with the sharp drop in performance level and performance

differential documented in Figure 1.

To further investigate whether our evidence reflects the adverse effects of cognitive aging

or cohort effects, we identify a scenario where cohort effects do not make a meaningful predic-

tion but the cognitive aging hypothesis makes a sharp prediction. Specifically, we assume that

portfolio size is a proxy for task difficulty and examine the effect of portfolio size on portfolio

30

performance differential that we attribute to cognitive aging. When an investor actively man-

ages a larger portfolio that requires greater attention and cognitive capacity, the cognitive aging

hypothesis predicts that the possibility of making mistakes would be greater among older in-

vestors. Consequently, the performance differential between younger and older investors would

increase with portfolio size. In contrast, there is no obvious birth cohort-based prediction for

the variation in performance differential with portfolio size.

In our last cohort related test, we include Portfolio Size×Age interaction variable in the skill

regression specification (column (6) in Table IV, Panel A). We find that the interaction term

has a significantly negative coefficient estimate (estimate = −0.032, t-stat = −3.987), while the

estimates of other variables in the model remain almost unchanged. Thus, consistent with the

cognitive aging hypothesis, older investors exhibit worse risk-adjusted performance when they

hold larger portfolios that are more difficult to manage.26 This evidence, however, does not have

a clear cohort-based explanation. Overall, the results from birth cohort related robustness tests

indicate that cohort effects are unlikely to successfully explain the observed negative relation

between age and investment skill.

VI. Economic Costs of Cognitive Aging

A. A Portfolio Based Approach

In this section, we quantify the economic costs associated with cognitive aging more accurately

using portfolio-based, time-series tests. An additional advantage of the portfolio-based analy-

sis is that it is insensitive to concerns about potential cross-sectional dependence in portfolio

performance.

We proceed as follows: First, we follow the standard imputation methodology (e.g., Skinner

(1987), Ziliak (1998), Browning and Leth-Petersen (2003)) and use the previously estimated

model of cognitive abilities (see Section V.C and Table V) to obtain an imputed cognitive ability

31

measure for each investor. We regress this imputed cognitive ability measure on investment

experience and obtain a residual cognitive ability measure that is orthogonal to experience.

Next, we sort investors into deciles based on their residual cognitive ability measures, where

group 1 consists of investors with low cognitive ability and group 10 consists of investors with

high cognitive abilities. Last, we compute the average performance of investors in each of the

ten cognitive ability categories and estimate the economic costs of aging.

We find that investors in the lowest cognitive ability decile earn a mean monthly return of

0.984%, investors in the highest cognitive ability decile earn a mean monthly return of 1.264%,

and the annualized performance differential of 3.360% (12×(1.264−0.984)) is statistically signif-

icant (t-stat = 2.181). The performance differentials are of similar magnitudes when we measure

the risk-adjusted performance using the four-factor alpha (annualized performance differential

= 3.240%, t-stat = 2.762) or the characteristic-adjusted returns (annualized performance differ-

ential = 3.363%, t-stat = 2.827). These performance estimates indicate that the economic costs

of cognitive aging are significant.

Examining the factor exposures of the cognitive ability sorted portfolios, we find that high

cognitive ability investors hold relatively riskier, smaller, and growth-oriented portfolios. For

instance, the four factor exposures (RMRF , SMB, HML, and UMD) for the lowest cognitive

ability decile portfolio are 1.083, 0.571, 0.314, and −0.218, respectively. In contrast, for the

highest cognitive ability decile portfolio, the corresponding factor exposures are 1.219, 0.677,

0.112, and −0.299, respectively. These factor exposure estimates are statistically significant and

the factor estimate differences between the high and the low cognitive ability decile portfolios

are also significant. This evidence is consistent with our evidence on investors’ stock preferences,

conditional upon age (see Section IV.A and Table II).

To examine whether the economic costs of aging are also economically significant for in-

vestors who hold larger portfolios, we compute the risk-adjusted performance measures, con-

ditional upon portfolio size. The results are shown in Figure 2. We find that the economic

cost of cognitive aging increases with portfolio size. As portfolio size increases, high (quintile 5)

32

cognitive ability investors perform better, low (quintile 1) cognitive ability investors do worse,

and the performance gap becomes wider. When portfolio size is below $10,000, the annualized

characteristic-adjusted return differential is 1.725% and it increases to 5.012% when the portfo-

lio size is above $50,000. When we use the four-factor alpha as the performance measure, the

cognitive aging related performance differentials for small, mid-sized, and large portfolios are

2.148%, 2.407%, and 4.613%, respectively.27

Collectively, the results from portfolio-based time-series tests indicate that investors who

do not experience the adverse effects of cognitive aging earn superior risk-adjusted returns.

Importantly and somewhat surprisingly, the economic costs of cognitive aging are larger (both

in percentage and dollar terms) among investors who hold larger portfolios. Those investors are

less likely to hold significant positions outside their brokerage accounts, especially during the

sample period when the median number of brokerage accounts varied between one and two.28

The performance differentials measured in percentage terms might not appear alarming, but

because older investors hold larger portfolios, the economic costs are even more significant when

measured in dollar terms.

B. Identifying the Components of Stock Selection Ability

To better understand how high cognitive ability investors generate superior portfolio perfor-

mance, we use the Daniel, Grinblatt, Titman, and Wermers (1997) decomposition to estimate

the three components of stock selection skill: characteristic selectivity (CS), characteristics tim-

ing (CT ), and average style (AS). A positive estimate for CS reflects stock selection ability

within the style portfolios, while a positive CT estimate provides evidence of style timing.

First, we sort investors into five or ten categories based on their residual cognitive ability

measures and construct an aggregate portfolio for each investor category by combining the

portfolios of all investors who belong to the group. Then, for each of those aggregate portfolios,

we compute the CS, CT , and AS measures. We find that high cognitive ability investors exhibit

greater ability to pick stocks within the styles. When we consider five portfolios, the annual CS

33

measures for the lowest and the highest cognitive ability quintile portfolios are −0.496% and

0.660%, respectively, and the difference of 1.156% is significant. As expected, the performance

differential is stronger (= 1.920%) when we consider cognitive ability sorted decile portfolios.

Examining the CT estimates for the cognitive ability sorted portfolios, we find that CT

estimates are uniformly negative for all portfolios. Thus, both high and low cognitive ability

investors lack characteristic timing abilities. However, the low cognitive ability investors have

more negative CT measure and exhibit worse timing abilities. For instance, the annual CT

measure for the lowest and the highest decile portfolios are −2.001% and −1.156%, respectively,

and the difference is positive (= 0.845%).

The AS estimates for the cognitive ability sorted portfolios exhibit less variation and are

similar. Nevertheless, the performance difference between the highest and the lowest cognitive

ability categories is positive. When we consider quintile portfolios, the annual AS differential

is 0.292% and when we consider decile portfolios, the differential is 0.429%. Overall, the per-

formance differentials between the highest and the lowest cognitive ability sorted quintile and

decile portfolios are 1.949% and 3.195%, respectively.

VII. Alternative Explanations and Robustness Checks

In this section, we conduct a wide array of tests to examine the robustness of our results

and attempt to further rule out alternative interpretations for our findings. The results are

summarized in Table VI, where for brevity, we only report the estimates for the six variables

that are most closely related to our aging related hypotheses.

A. Alternative Skill Measures

In the first set of tests, we consider other investment skill measures. First, we compute a trading-

based skill measure that is not strongly correlated with our previous performance-based skill

measures and does not depend upon our ability to observe investors’ entire financial portfolios.

34

This skill measure reflects the belief that investors who have superior stock selection ability are

likely to buy stocks that perform better than the stocks they sell. Our choice is motivated by

Odean (1999) and Barber and Odean (2001), who use a similar measure to identify the stock

selection ability of investors.

Specifically, we use the mean k-day post-trade buy-sell return differential (PTBSD(k)) as a

measure of investment skill. We choose two different values of k (k = 5 and 10), because using the

same dataset as ours, Coval, Hirshleifer, and Shumway (2005) show that the trading performance

of individual investors declines after about two weeks. When PTBSD(5) or PTBSD(10) is

used as a dependent variable in the skill regression, similar to the results from previous skill

measures, we find that the Age and Investment Experience have opposite signs (see tests (1) and

(2) in Table VI). The interaction terms mostly have the expected signs, though their estimates

are statistically weaker. This evidence indicates that older investors trade less (see Table III),

but when they do trade, they make worse buy and sell decisions. The stocks they purchase

under-perform the stocks they sell by a larger magnitude.

Next, we examine investors’ market timing abilities using the two Graham-Harvey perfor-

mance metrics (Graham and Harvey (1996, 1997)). We re-estimate the skill regression and

find that, in both instances, age and investment experience maintain their opposite signs (see

tests (3) and (4)). In addition, the interaction term estimates are very similar to the respective

estimates in the alpha skill regression reported in Table IV, Column (4). These results are

consistent with our second main hypothesis and indicate that market timing skill improves with

experience but deteriorates with age due to the adverse effects of cognitive aging.

B. An Alternative Experience Measure

In our second robustness test, we define an alternative experience measure using our main

investment experience proxy (number of days since account opening date) and self-reported

measures of investment knowledge and experience. For a small sub-set of investors, we know

whether investors believe that they have extensive, good, limited, or zero investment experience.

35

A similar self-reported measure reflects their self-assessment of investment knowledge. Using

these two self-reported measures, we construct an indicator variable that is set to one for investors

who have either good or extensive investment knowledge or experience. We also define a second

indicator variable that is set to one for investors who hold the brokerage account for at least

five years. Our new experience measure is the sum of the two indicator variables.29

When we replace the investment experience proxy in the skill regression with this new expe-

rience variable, we still find that Age has a significantly negative coefficient estimate (coefficient

= −0.054, t-stat = −3.690) and Experience has a significantly positive coefficient estimate (co-

efficient = 0.033, t-stat = 2.390). The other main variables in the skill regression specification

maintain their original signs and significance levels (see test (5)). This evidence indicates that

our key results are robust and do not depend upon the specific choice of the investment experi-

ence proxy.

C. Aging Effects or Informational Illiteracy?

In the third robustness test, we entertain another cohort-based explanation for the negative age-

skill relation. Specifically, we examine whether older investors make worse investment decisions

because they are slower to adopt new technology such as the Internet and not due to cognitive

aging. It is possible that older investors who belong to a cohort from the “Radio and Television”

era and are not as technologically savvy as the cohort of younger investors from the “Computers

and Internet” era. Consequently, older investors could experience higher search costs and make

their decisions using stale and less accurate information signals.

We consider a subset of investors who are technologically savvy and have used the Internet

to execute trades in their brokerage account. If the adverse effects of aging are visible even

among this set of investors with relatively higher levels of informational literacy, it is unlikely

that cohort induced differences in technology adoption propensity can successfully explain our

findings. When we use the four-factor alpha skill measure to estimate the skill regression using

the sub-sample of Internet users only, we find that Age and Investment Experience maintain

36

their opposite signs (see test (6)). Age has a coefficient estimate of −0.063 (t-stat = −3.168)

and Experience has a coefficient estimate of 0.048 (t-stat = 2.653). The other main variables

in the skill regression specification maintain their original signs and significance levels. These

results are qualitatively similar to our baseline estimates reported in Table IV and indicate that

informational literacy associated with an age cohort is unlikely to be an appropriate explanation

for our findings.

D. Split Sample Tests

In our fourth robustness test, we re-estimate the skill regression for two sub-periods. The

1991 to 1996 sample period encapsulates two distinct market conditions: (i) a relatively flat

market during the first half of the sample period, following the 1990 NBER recession, and (ii)

an increasing market during the second half of the sample period, representing the start of the

“bubble” period. One might be concerned that the negative age-skill relation we find results from

the relatively conservative (i.e., less risky) investments by older investors during bullish market

conditions. To examine whether the adverse effects of cognitive aging are significant during

both periods of weak and strong stock market performance, we estimate the skill regression for

the 1991 to 1993 and the 1994 to 1996 sub-periods using the characteristic-adjusted portfolio

returns. We use the characteristic-adjusted performance measures because the four-factor alpha

estimates would be noisier with only three years of data.

The skill regression estimates for the two sub-samples indicate that the adverse effects of

cognitive aging and the positive effects of learning are present in both time-periods (see tests (7)

and (8)). Both age and experience variables have significant coefficient estimates. Interestingly,

the age-race/ethnicity interaction terms have statistically weak coefficient estimates in the full-

sample regression but they have the expected negative signs during the 1994 to 1996 sub period.

Taken together, the sub-period estimates indicate that the negative age-skill relation we find

cannot be attributed to the bullish market conditions during the latter part of the sample

period.

37

E. Differential Skill in Identifying Superior Local Stocks

The fifth robustness test focuses on the performance of local investments. Ivkovic and Weisben-

ner (2005) show that, on average, the local stock investments of individual investors perform

better than their non-local investments. To examine whether the negative age-skill relation hold

in both local and non-local settings, we compute the four-factor alpha for each investor’s local

portfolio. The local portfolio represents the part of the portfolio that contains stock investments

in firms located within a 100 mile radius of investor’s location.30 We re-estimate the skill re-

gressions using the local alpha measure as the dependent variable. The correlation between the

local and the total alpha measures is positive (= 0.513) but not very high.

The skill regression estimates are again consistent with our second main conjecture. We find

that age and investment experience estimates have opposite signs, and the age-race/ethnicity

interaction terms have negative coefficient estimates (see test (9)). The Age×Low Income and

Age×Low Education interaction terms have the expected negative signs but those estimates are

statistically insignificant. This evidence indicates that older investors experience the adverse

effects of cognitive aging even in their local stock investment decisions.

F. Controls for Liquidity and Industry Exposures

In the next robustness test, we further ensure that our results are not influenced by the ex-

ceptional performance of certain styles or industries during the relatively short six-year sample-

period. We follow the Pastor and Stambaugh (2002) and Pastor and Stambaugh (2003) method-

ologies and compute portfolio alphas after employing controls for industry exposures and liquid-

ity. We estimate skill regressions using this eight-factor alpha and find that Age is still negatively

related to investment skill (estimate = −0.047, t-stat = −3.745), while Investment Experience

is still positively related to investment skill (estimate = 0.022, t-stat = 2.314). Furthermore,

the interaction terms maintain their negative coefficient estimates (see test (10)).

For additional robustness, we follow an alternative approach to control for the effects of indus-

tries. For each investor, we compute the mean portfolio weight allocated to the 48 Fama-French

38

industries (Fama and French (1997)) and employ them as additional independent variables in the

skill regressions. In untabulated results, we find that many of these industry weights have large

and significant coefficient estimates. For instance, technology stocks in the electronic equipment

industry has a strong positive coefficient estimate (estimate = 0.114, t-stat = 10.254) while util-

ities industry has a strong negative coefficient estimate (estimate = −0.152, t-stat = −12.773).

However, the age, experience, and relevant interaction variables still maintain their signs and

statistical significance. Thus, the exceptional performance of one or more industries during the

sample period does not significantly influence our skill regression estimates.

G. Lack of Skill or Lack of Effort?

The seventh robustness test examines the “play money” hypothesis. One might argue that

the negative skill-aging relation we find is not too surprising or economically very meaningful

because the portfolios we analyze represent investors’ play money accounts meant primarily for

gambling and entertainment purposes. The bulk of investors’ actual investments including their

retirement accounts are held elsewhere, which we cannot observe.

To examine whether the weaker investment skill of older investors can be attributed to their

lack of interest in their brokerage portfolios, we consider a sub-sample of investors who hold

larger portfolios in comparison to their income levels. Specifically, we use the four-factor alpha

skill measure and re-estimate the skill regressions for the sub-sample of investors whose mean

portfolio size to annual income ratio (i.e., SIR) is greater than or equal to 1.23 (the top two-third

of investors). These equity portfolios are unlikely to represent investors’ play money accounts

and are less likely to be ignored.

The skill regression estimates for the large portfolio sub-sample indicate that the sub-sample

coefficient estimates are similar to the full sample results (see test (11)). For instance, Age has

a coefficient estimate of −0.053 (t-stat = −4.759) and Investment Experience has a coefficient

estimate of 0.018 (t-stat = 1.996) in the alpha regression. Additionally, two of the four interac-

tion terms have the expected negative signs. Thus, our key results are unlikely to be successfully

39

explained by the play money hypothesis.

H. Are the Results Driven by Investors Located in California?

In the eighth robustness test, we examine whether our results are influenced by the strong

concentration of investors from California because a considerable portion (27.25%) of our sample

is located in California. To guard against this possibility, we exclude all investors who reside

in California and re-estimate the skill regression using the four-factor alpha skill measure. The

results for the non-Californian sub-sample are similar to the full sample results (see test (12)).

Age has a coefficient estimate of −0.044 (t-stat = −2.797) and Investment Experience has a

coefficient estimate of 0.017 (t-stat = 2.651) in the alpha regression. This result indicates that

the geographical concentration of our sample investors is unlikely to successfully explain the

negative age-skill relation.

I. Is the Age on the Account Opening Date An Indicator of Skill?

In the last robustness test, we examine whether our main results are influenced by a sample

selection bias. In particular, one might be concerned that investor’s age on account opening

date might be an indicator of skill. All else equal, investors who open the brokerage account at

an older age would have lower investment skill. Thus, the investment skill differences between

older and younger investors after accounting for experience might not reflect the adverse effects

of cognitive aging but could merely reflect the sample selection bias.

To ensure that our results not influenced by the potential sample selection bias, we compute

the age of each investor on the account opening date (= Age in June 1997 − Investment Expe-

rience) and estimate skill regressions for younger, middle-aged, and older investors sub-samples.

We use the age on the account opening date to define the three sub-samples. In untabulated

results, we find that in both diversification skill and stock selection skill regressions, the age and

experience variables maintain their opposite signs and magnitudes. This evidence indicates that

40

our results do not reflect skill differences that can be attributed to investor’s age on account

opening date.

Collectively, the additional robustness test results indicate that the empirical support for the

unconditional (H2) and conditional (H2cond) hypotheses is strong and the results are remarkably

consistent with the extant psychological evidence. Our findings are not sensitive to the choice of

skill measures, potential error in skill measurement, choice of the risk adjustment methodology,

specific market conditions, investors’ lack of interest in relatively small brokerage portfolios, and

the geographical concentration of our sample investors.

VIII. Summary and Implications of Our Research

This is the first study to examine the potential role of cognitive aging on the stock investment

decisions of older investors. We investigate whether older individual investors make better

investment choices because of greater investment experience or whether their investment skill

deteriorates with age due to the adverse effects of cognitive aging. This is an important issue

that has implications for how individual investors should structure their portfolios over time,

the type of investment advice they should seek over their lifetime, and the potential effects of

changes in government policy on investment generated retirement income.

Our evidence indicates that older and more experienced investors hold less risky portfolios,

exhibit stronger preference for diversification, trade less frequently, exhibit greater propensity for

year-end tax-loss selling, and exhibit weaker behavioral biases such as the disposition effect and

familiarity bias. Thus, their choices reflect greater knowledge about investing. But consistent

with the cognitive aging hypothesis, we also find that older investors have worse investment

skill, where the skill deteriorates sharply around the age of 70. Examining the economic costs

of aging, we find that older investors earn about 3-5% lower annual return on a risk-adjusted

basis. Collectively, our evidence indicates that older investors’ portfolio choices reflect greater

knowledge about investing but their investment skill deteriorates with age due to the adverse

41

effects of cognitive aging.

These results could potentially be used to improve the investment decisions of older investors.

We do not prescribe that older investors should stop making independent investment decisions.

Rather, based on the evidence, our hope is that older people would recognize the adverse effects

of cognitive aging and would try to compensate for those effects, perhaps by seeking advice

from a financial advisor or some other qualified investment professional. An investment refresher

course that highlights the adverse effects of cognitive aging and prescribes effective compensating

mechanisms might also be helpful. This may especially be a wise decision for investors who hold

portfolios larger than those examined in this study. Our performance results also indicate that

while most investors in our sample would benefit from holding a passive index fund, the potential

benefits of passive investing are likely to be higher for older investors.

In broader terms, our empirical findings could help us better understand the stock market

participation puzzle. Theoretical models typically have the greatest difficulty in explaining the

participation rates in the extreme age categories (e.g., Gomes and Michaelides (2005)). Based on

our findings, we conjecture that younger investors would stay away from the stock market due to

their lack of investment experience, while older investors would be less willing to participate due

to a perception of declining cognitive abilities. A theoretical model that synthesizes the positive

effects of experience and adverse effects of cognitive aging may provide a fresh perspective into

the stock market participation and the broad asset allocation decisions over the life-cycle.

Our empirical evidence also provides specific guidance for refining asset pricing models that

incorporate the effects of aging. Previous theoretical models have examined the aggregate effects

of aging on the stock market behavior (e.g., Bakshi and Chen (1994), Poterba (2001), Goyal

(2004)) through the channel of risk aversion. Our results indicate that age is likely to influence

asset returns through an additional channel. Specifically, if older investors become aware of their

declining investment skill, the perceived costs for stock market participation would increase,

and those investors would demand a higher premium for investing in the stock market. In

this scenario, stock market returns could increase as the population ages, even when there is no

42

substantial increase in people’s risk aversion. Additionally, our evidence on the stock preferences

of older investors provide guidance about the segments of the market (e.g., high dividend yield

and less risky stocks), where the effects of aging on stock returns are likely to be stronger.

We conclude the paper with a caveat. Although our results are strongly consistent with

the cognitive aging hypothesis, some amount of caution must be exercised while interpreting

this evidence because we cannot directly measure the degree of cognitive decline among older

investors. In addition, because we use a relatively short six-year panel to identify the adverse

effects of cognitive aging, in spite of our numerous attempts to rule out alternative explanations

for our results based on cohort and time effects, some concerns might remain. Nevertheless, given

the remarkable similarities between our results and the evidence from psychological research on

aging, the footprints of cognitive aging in investment decisions appear strong and difficult to

ignore.

43

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Notes

1According to the 2004 Federal Interagency Forum on Aging-Related Statistics, older people (people aged

65 and above) represented about 12% of the population in 2000, but by 2030, their proportion is expected to

increase to about 20%. During the same period, the proportional share of African Americans and Hispanics in

the older population is expected to increase from 14% to 31%.

2The brokerage account opening date can be prior to the sample start date of January 1991. The earliest

accounts were opened in 1972 and all investors in the sample have an account opening date prior to 1992. About

88% of investors in the sample opened their accounts prior to the beginning of the sample period.

3In a related study, Agarwal, Driscoll, Gabaix, and Laibson (2007) examine whether the interaction between

cognitive abilities and experience generates a hump-shaped pattern in financial sophistication, which influences

the prices people pay for financial services.

4Some theoretical models (e.g., Mossin (1968), Samuelson (1969), Merton (1969)) also predict that portfolio

holdings of investors would remain constant with age. See Ameriks and Zeldes (2004) for an excellent review of

this literature.

5There is an interesting (though imperfect) analogy between the investment behavior of older investors we are

trying to capture and the driving behavior of older people. Older drivers may accumulate more driving knowledge

because of their greater driving experience, but they may not be able to apply that knowledge effectively due

to a decline in their physical abilities. In a similar manner, older investors would have greater knowledge

about investing, but they may still fail to apply them effectively due to decline in their general intelligence and

information processing abilities. The analogy suggests that just as older drivers face additional aging related

risks on the road, older investors are likely to expose their portfolios to non-compensated risks due to the adverse

effects of cognitive aging.

6Because the demographic information is available for only a subset of investors in the sample (e.g., both age

and income measures are available for only 31,260 investors), the number of observations in our cross-sectional

regressions depends upon the subset of demographic variables included. See Barber and Odean (2001, Section

II.A) for additional details about the available demographic information.

7See Ivkovic, Poterba, and Weisbenner (2005) and Ivkovic, Sialm, and Weisbenner (2008) for additional

50

discussions on the representativeness of the brokerage data.

8The U.S. Census data are available at http://www.census.gov/main/www/cen1990.html. The SHARE

data are described in Christelis, Jappelli, and Padula (2007) and are available at http://www.share-project.org/.

Professor Kenneth French’s data library is available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

Professor Russ Wermer’s data library is available at http://www.smith.umd.edu/faculty/rwermers/ftpsite/Dgtw/coverp

9The excess portfolio weight allocated to stock i in month t is given by: EW ipt =wipt−wimt

wimt× 100, where

wipt is the actual weight assigned to stock i in group portfolio p in month t and wimt is the weight of stock i in

the aggregate market portfolio in month t.

10The results are remarkably similar when we use other age categories. Specifically, we examined the robust-

ness of our results using the following three age groups: (i) 20-40 (weak retirement motive), (ii) 41-65 (strong

retirement motive), and (iii) above 65 (retired).

11Optimal trading behavior in presence of taxes requires skill (e.g., Constantinides (1983, 1984), Ivkovic,

Poterba, and Weisbenner (2005)). However, such optimal response to taxes would lead to higher risk-adjusted

performance, which our risk-adjusted performance measures are likely to capture (see Section V).

12We obtain similar results when we use other measures (e.g., normalized portfolio variance) to capture the

preference for diversification. Also, see the results in Table V of Goetzmann and Kumar (2008).

13The monthly portfolio turnover rate is the average of purchase and sales turnover rates. The purchase

turnover rate in month t is the ratio of the dollar value of purchases in month t (beginning of month stock prices

are used to compute the value) and the dollar value of the portfolio at the end of month t−1. The sales turnover

rate is defined in an analogous manner.

14In untabulated results, we find that both older and experienced investors are more likely to invest in mutual

funds. However, older investors exhibit a greater propensity to invest in index funds, while experienced investors

exhibit a stronger preference for other types of funds.

15See Bailey, Kumar, and Ng (2008) for additional results on the relation between age and foreign stock

holdings. Bailey, Kumar, and Ng (2009) provide additional evidence on the effect of age on the mutual fund

choices of individual investors.

16The disposition effect evidence is also reported in Dhar and Zhu (2006), although they do not focus on the

51

opposite effects of cognitive aging and investment experience.

17The cognitive ability index is constructed using self-reported measures of ability on a five point scale. Specif-

ically, the Cognitive Ability Index = (Memory − Do Not Get Abstract Idea + Rich Vocabulary + Use Difficult

Words)/4. It is positively correlated with the experience measure but negatively correlated with age.

18Goetzmann, Li, and Rouwenhorst (2005) show that the total portfolio variance can be reduced by increasing

the number of stocks in the portfolio and by a proper selection of stocks such that the average correlation among

stocks in the portfolio is lower. Variance reduction through proper stock selection reflects “skill” while addition

of stocks in the portfolio without a reduction in the average portfolio correlation reflects a “passive” form of

diversification.

19Even when we consider other performance benchmarks that include industry and liquidity factors, our key

results remain qualitatively similar. See Section VII.F.

20Consistent with our evidence, using household-level data from Sweden, Calvet, Campbell, and Sodini (2007)

show that older investors make cautious but relatively less efficient investment choices. Also, see Campbell

(2006).

21In a different context, Chevalier and Ellison (1999) find that, keeping experience and other characteristics

constant, older mutual fund managers exhibit worse performance than younger managers. They find this evidence

puzzling and attribute it to managers’ career concerns. However, the evidence is also consistent with our

unconditional hypothesis, which posits that skill varies inversely with age and positively with experience.

22Also, see Bailey, Kumar, and Ng (2009) for additional evidence on a negative relation between age and

mutual fund performance.

23The correlation between the four-factor alpha and the characteristic-adjusted performance measures is pos-

itive (0.592) but not extremely high.

24To eliminate potential concerns about reverse causality (portfolio size is larger because of better portfolio

performance and not vice versa), we use the portfolio size from the first month the investor enters the sample.

25The results are very similar when the skill measure is the four-factor alpha computed using net returns. The

coefficient estimate of Age is −0.057 (t-stat = −5.366) while the coefficient estimate of Investment Experience is

0.030 (t-stat = 4.380). The interaction terms have the expected signs too. For brevity, we do not tabulate those

52

results.

26Also, see Figure 2. We find similar results when we use the number of stocks in the portfolio to quantify the

difficulty level of managing a portfolio. The coefficient estimate is −0.030 and t-stat = −3.008.

27As before, we find qualitatively similar results when we use the number of stocks in the portfolio to quantify

the difficulty associated with managing a portfolio.

28According to the 1992 Survey of Consumer Finances (SCF), the median U.S. household held only one

brokerage account (mean = 1.57) in 1992 (about 62% of households had only one brokerage account) and the

1995 SCF indicates that the median number of brokerage accounts increased to two (mean = 2.62) in 1995.

29We find similar results if we define the new experience measure as the interaction between the two indicator

variables.

30Following Ivkovic and Weisbenner (2005), we choose the 100-mile cutoff to define local and non-local portfolio

components, but the results are similar when we use a 250-mile cutoff.

53

TABLE I. – SUMMARY STATISTICS: AGE SORTED INVESTOR GROUPS

Age Group Portfolio Size Income Wealth SIR SWR Experience

Panel A: All Investors

Q1 (20-38) $23,372 $90,146 $196,765 0.414 0.283 5.46

Q2 (39-46) $23,372 $98,619 $243,081 0.377 0.246 7.68

Q3 (47-52) $29,270 $101,086 $247,701 0.462 0.304 8.92

Q4 (53-59) $32,543 $93,363 $296,595 0.554 0.298 9.01

Q5 (60-94) $49,274 $70,700 $360,403 1.096 0.346 10.49

Mean $31,566 $90,782 $268,909 0.581 0.295 8.71

Panel B: Investors With Age 60 or Above

Q1 (60-62) $37,652 $87,134 $340,955 0.599 0.293 9.85

Q2 (63-64) $39,678 $74,890 $356,931 0.765 0.322 10.39

Q3 (65-70) $48,416 $72,833 $409,153 1.040 0.313 10.33

Q4 (71-74) $48,556 $67,574 $350,882 0.984 0.338 10.45

Q5 (75-94) $64,526 $64,111 $334,917 1.469 0.464 10.87

Portfolio size is the mean portfolio size of the investors in the group during the sample period. Income is the

annual household income and wealth is the self-reported net worth reported at the account opening date. SIR

is the portfolio size to income ratio, and SWR is the portfolio size to wealth ratio. Investment experience is the

number of years between the account opening date and December 31, 1996. In Panel A (Panel B), there are

5,404 (1,351) observations in each group.

54

TABLE II. – AGE AND STOCK PREFERENCES: PANEL REGRESSION ESTIMATES

Age Groups

Variable (1): 20-38 (2): 60-94 (3): 75-94 (2)−(1) (3)−(1)

Mean Return −0.118 −0.146 −0.134 −0.016 −0.021

−14.295 −14.293 −13.406 −1.747 −2.356

Idiosyncratic Volatility 0.139 0.128 0.116 −0.046 −0.050

24.124 18.095 16.753 −7.138 −7.880

Skewness 0.052 0.018 −0.019 −0.037 −0.060

11.604 3.254 −3.538 −7.266 −12.018

Kurtosis −0.075 −0.047 −0.015 0.040 0.060

−15.670 −7.984 −2.523 7.513 11.314

Stock Price −0.033 −0.054 −0.055 −0.014 −0.013

−11.268 −14.903 −15.520 −1.213 −0.859

Market Beta 0.095 0.033 0.007 −0.068 −0.081

29.707 8.383 1.881 −19.061 −22.980

Log(Firm Size) −0.128 −0.104 −0.007 0.026 0.115

−31.992 −21.011 −1.348 3.415 26.088

Book-To-Market Ratio −0.058 −0.025 −0.032 0.039 0.033

−19.793 −6.940 −9.199 11.965 10.172

Past 1-Month Stock Return 0.003 0.009 0.010 0.002 0.004

0.882 2.209 2.448 0.685 1.009

Past 12-Month Stock Return 0.001 0.025 0.016 0.014 0.006

0.134 4.607 2.996 2.789 1.286

S&P500 Dummy 0.008 0.067 0.053 0.046 0.039

4.534 20.810 16.851 5.039 5.682

Monthly Turnover 0.062 −0.003 −0.005 −0.051 −0.062

23.627 −1.564 −2.537 −5.876 −8.604

Dividend Yield 0.006 0.018 0.030 0.015 0.021

0.450 3.470 3.701 2.455 2.818

Month Fixed Effects Yes Yes Yes Yes Yes

Number of Observations 113,269 113,269 113,269 113,269 113,269

Adjusted R2 0.056 0.031 0.011 0.010 0.024

This table reports the panel regression estimates for different age-based investor groups, where the excess weight

assigned to a stock in the aggregate group portfolio is the dependent variable. The group portfolio is formed by

55

combining the portfolios of all investors who belong to the group. Three aggregate group portfolios are considered:

the aggregate portfolio of younger (age range 20-38), older (age range 60-94), and very old (age range 75-94)

investors. The excess portfolio weight allocated to stock i in month t is given by: EW ipt =wipt−wimt

wimt× 100,

where, wipt is the actual weight assigned to stock i in group portfolio p in month t and wimt is the weight of stock

i in the aggregate market portfolio in month t. The mean return, idiosyncratic volatility, skewness, kurtosis,

and the price of the stock is used as independent variables. Additionally, the following stock characteristics are

employed as control variables: (i) market beta, which is estimated using past 60 months of data, (ii) firm size,

(iii) book-to-market ratio, (iv) short-term momentum (past one-month stock return), (v) longer-term momentum

(past twelve-month stock return), (vi) an S&P500 dummy which is set to one if the stock belongs to the S&P500

index, (vii) monthly volume turnover, and (viii) the annual dividend yield. The t-statistics for the coefficient

estimates are shown in smaller font below the estimates, where we use the non-parametric approach of Driscoll

and Kraay (1998) to obtain corrected standard errors. We winsorize all variables at their 0.5 and 99.5 percentile

levels and the independent variables are standardized.

56

TABLE III. – RULE OF THUMB CROSS-SECTIONAL REGRESSION ESTIMATES

Variable (1): NSTKS (2): NSTKS (3): TURN (4): TURN (5): TAX (6): PDY

Panel A: Main Rules of Thumb Regression Estimates

Intercept 4.308 4.392 5.344 4.121 0.157 1.773

18.967 20.715 27.395 11.525 14.211 18.467

Age 0.476 0.186 −0.407 −0.183 0.016 0.116

20.150 7.454 −7.347 −4.355 5.696 10.537

Investment Experience 0.517 0.423 −0.223 −0.177 0.006 −0.013

21.294 19.113 −3.922 −4.749 2.311 −2.285

Income 0.020 −0.100 0.003 −0.035

2.019 −2.665 1.329 −3.520

Education −0.035 −0.014 −0.004 −0.001

−1.878 −0.376 −1.685 −0.127

Male Dummy 0.013 0.157 0.006 −0.040

1.345 4.115 2.655 −0.969

Retired Dummy 0.005 0.006 −0.001 0.032

0.210 0.168 −0.333 3.265

Portfolio Size 1.642 0.282 0.075 0.116

30.266 7.154 22.960 11.218

Portfolio Turnover −0.399 0.093 −0.066

−17.697 28.848 −6.589

Portfolio Dividend Yield 0.152 −0.286 −0.003

5.922 −6.589 −1.221

Portfolio RMRF Exposure −0.020 0.509 0.009 −0.215

−0.821 12.291 3.149 −19.833

Portfolio SMB Exposure 0.304 0.828 0.021 −0.814

10.491 17.023 6.684 −20.737

Portfolio HML Exposure 0.052 −0.609 −0.011 0.666

1.903 −13.152 −3.695 19.019

Portfolio UMD Exposure 0.051 0.132 −0.001 −0.116

2.129 3.242 −0.071 −10.827

Mutual Fund Holdings 0.127 0.215 0.010 0.027

6.276 5.885 3.987 2.723

Number of Investors 27,716 19,906 27,716 19,906 19,906 19,906

Adjusted R2 0.044 0.252 0.035 0.158 0.120 0.282

Continued. . .

57

Dependent Variable Intercept Age Experience

Panel B: Other Rules of Thumb Regression Estimates

(1) Number of Asset Classes 2.545 0.139 0.073

24.956 13.035 6.871

(2) Mutual Fund Portfolio Expense Ratio × 100 0.856 −0.026 −0.013

11.668 −9.371 −4.601

(3) Weight in Foreign Stocks × 100 3.575 0.672 1.384

17.925 3.053 4.224

(4) Adjusted Disposition Effect × 100 1.780 −7.849 −1.467

3.527 −6.632 −2.235

(5) Local Bias × 100 29.493 −0.822 −0.434

11.590 −3.866 −2.511

(6) Margin Account Dummy 0.577 −0.023 0.007

20.744 −8.178 2.531

(7) Short-Sell Dummy 0.096 −0.017 0.015

18.239 −4.330 8.125

(8) Option Trade Dummy 0.089 −0.018 0.019

15.697 −8.735 9.701

Panel C: Logit Estimates using the Dutch DNB Data

(1) Mutual Fund Participation Dummy −5.587 0.022 0.473

−12.552 4.851 4.746

(2) All Asset Classes Participation Dummy −9.788 0.053 0.613

−7.186 3.819 2.067

This table reports the estimates from cross-sectional regressions, where a measure of investment choice reflecting

a “rule of thumb” is the dependent variable. In Panel A, we consider four different measures: (i) average number

of stocks in the portfolio (NSTKS), (ii) portfolio turnover (TURN), (iii) proportion of “losers” (stock investments

where an investor has experienced a loss) realized in the month of December (TAX), and (iv) portfolio dividend

yield (PDY). All measures are obtained for each investor using their choices during the sample period. In Panel

B, we consider the following measures: (i) number of asset classes in which the investor has at least one trade

during the sample period, (ii) the sample-period expense ratio of the investor’s mutual fund portfolio, (iii) the

proportion of equity portfolio invested in foreign stocks, (iv) local bias, measured as the proportion of equity

58

portfolio that is invested in stocks within a 100-mile radius, (v) the peer-group adjusted disposition effect (ADE)

measure, defined as the difference between an investor’s actual propensity to realize gains and the expected

propensity to realize gains (see Kumar and Lim (2008) for details), (vi) margin fund dummy that is set to one

if the investor holds a margin account, (vii) short-sell dummy that is set to one if the investor holds a short

position at least once during the sample-period, and (viii) option trade dummy that is set to one if the investor

executes an option trade at least once during the sample-period. In Panel C, the dependent variable is either

(i) the mutual fund participation dummy (set to one if the investor holds any type of mutual fund) or (ii) the

“all asset classes” participation dummy (set to one if the respondent holds stocks, bonds, and mutual funds) in

the 2005 Dutch DNB Household Survey data. The independent variables used in Panels A and B are described

in Section IV.B. In Panel C, the independent variables are age, self-reported knowledge of financial markets

(proxy for investment experience), income, education level, gender, and retirement dummy. The t-statistics for

the coefficient estimates are shown in smaller font below the estimates, where robust, clustered standard errors

are used to account for potential cross-sectional dependence within zip codes. We winsorize all variables at their

0.5 and 99.5 percentile levels and the independent variables are standardized. In Panel C, we estimate a logit

model and do not standardize the variables. We report the z-statistics for the coefficient estimates based on

robust standard errors. In Panels A and B, the individual investor data are from a large U.S. discount brokerage

house for the period from 1991 to 1996. In Panel C, we use the 2005 Dutch DNB Household Survey data.

59

TABLE IV. – INVESTMENT SKILL CROSS-SECTIONAL REGRESSION ESTIMATES

SR (1-2) Alpha (3-4) Char Adj (5-8) Diff (9)

Variable (1) (2) (3) (4) (5) (6) (7) (8) (9)

Panel A: Baseline Specifications

Intercept 0.101 0.102 −0.341 −0.340 0.006 −0.001 0.031 0.001 0.006

13.173 9.568 −14.285 −13.099 0.699 −0.101 0.448 0.005 0.193

Age −0.001 −0.014 −0.042 −0.051 −0.044 −0.054 −0.063 −0.045 −0.077

−0.935 −3.355 −5.047 −4.735 −7.293 −2.945 −2.257 −4.636 −3.388

Investment Experience 0.011 0.010 0.010 0.020 0.037 0.027 0.028 0.026 0.028

11.644 9.450 1.184 2.283 6.053 3.891 2.289 3.938 3.103

Over 70 Dummy −0.007 −0.025 −0.020 −0.022 −0.014 −0.019

−1.483 −2.073 −2.163 −2.886 −2.592 −2.167

Income 0.001 0.001 0.011 0.004 −0.001 0.018

0.824 0.062 1.112 0.470 −0.108 2.013

Low Income Dummy −0.002 −0.004 −0.009 −0.011 −0.010 −0.008

−1.223 −0.275 −0.773 −1.004 −0.155 −0.218

Age × Low Income −0.012 −0.025 −0.014 −0.022 −0.023 −0.006

−2.033 −2.674 −1.996 −2.242 −2.367 −1.791

Education 0.011 0.014 0.017 0.013 0.013 0.014

1.882 2.527 2.717 2.089 2.129 1.529

Low Education Dummy −0.010 −0.012 −0.014 −0.015 −0.011 −0.025

−1.809 −1.813 −1.798 −1.401 −1.636 −1.510

Age × Low Education −0.011 −0.003 −0.005 −0.004 −0.004 −0.005

−1.789 −1.250 −2.719 −2.242 −1.843 −1.942

Male Dummy −0.001 −0.001 −0.006 −0.021 −0.011 −0.013

−0.550 −0.108 −0.945 −1.306 −1.816 −0.772

Retired Dummy 0.001 0.007 0.004 −0.010 0.002 −0.006

0.072 0.760 0.504 −0.957 0.391 −0.818

Hispanic Dummy −0.002 −0.003 0.009 −0.007 −0.018 −0.008

−0.350 −0.650 0.220 −1.072 −1.667 −0.309

African American Dummy −0.005 −0.016 −0.012 −0.003 −0.014 0.006

−1.038 −1.403 −1.133 −0.879 −1.084 0.517

Age × Hispanic −0.004 −0.034 −0.025 −0.017 −0.020 −0.036

−3.568 −3.516 −3.111 −2.876 −2.524 −2.488

Age × African American 0.002 0.010 0.009 −0.007 −0.008 −0.013

0.437 0.588 1.108 −1.035 −1.562 −1.876

(For brevity, the coefficient estimates of control variables are suppressed.)

Number of Investors 27,716 19,906 27,716 19,906 27,716 19,906 1,186,835 19,906 18,367

Adjusted R2 0.015 0.055 0.014 0.254 0.028 0.090 0.061 0.086 0.055

60

Skill Skill Difference

Variable (1): Alpha (2): Char Adj (3): Net Char Adj (4): Char Adj (5): Net Char Adj

Panel B: Specifications with Quadratic Age

Intercept −0.368 −0.016 −0.013 0.008 −0.017

−18.877 −0.656 −1.089 0.190 −1.099

Age −0.044 −0.064 −0.061 −0.079 −0.073

−4.316 −6.287 −4.521 −3.371 −3.066

Age2 −0.027 −0.018 −0.020 −0.044 −0.032

−2.922 −1.838 −2.157 −2.356 −2.624

Investment Experience 0.030 0.036 0.029 0.039 0.041

2.940 6.001 4.965 3.163 3.760

Over 70 Dummy −0.024 −0.026 −0.019 −0.017 −0.014

−2.296 −2.028 −2.614 −2.899 −1.834

(For brevity, other coefficient estimates are suppressed.)

The dependent variable is either a measure of investment skill or skill difference across the two halves of the

sample period. The following measures of investment skill are considered: (i) the monthly Sharpe ratio (SR),

(ii) the four factor alpha (Alpha), and (iii) the average characteristic-adjusted monthly portfolio return (Char

Adj). The four factor alpha is obtained by fitting a four-factor time-series model to the monthly portfolio return

series of each investor over the period the investor is active. All independent variables are defined in Section

V.C. In Column (7) of Panel A, we present panel regression estimates, where the skill measure is the monthly

characteristic-adjusted returns. In this specification, the factor exposures are excluded from the set of control

variables. In Column (8) of Panel A, the skill measure is the average net, characteristic-adjusted return. The

t-statistics for the coefficient estimates are shown in smaller font below the estimates, where robust, clustered

standard errors are used to account for potential cross-sectional dependence within zip codes. We winsorize all

variables at their 0.5 and 99.5 percentile levels and the independent variables are standardized.

61

TABLE V. – DETERMINANTS OF COGNITIVE ABILITIES

Cognitive ability measure is:

Variable Verbal Quantitative Memory Combined

Intercept −0.001 −0.005 −0.003 0.001

−0.080 −0.754 −0.571 0.118

Wealth 0.049 0.020 0.012 0.031

8.038 3.271 1.963 5.628

Income 0.047 0.053 0.002 0.041

7.818 8.482 0.372 7.230

Education 0.365 0.313 0.312 0.398

25.991 16.255 17.306 25.216

Age −0.129 −0.160 −0.239 −0.211

−13.178 −15.718 −24.088 −23.039

Retired Dummy −0.081 −0.065 −0.011 −0.056

−11.393 −10.394 −1.182 −9.953

Over 70 Dummy −0.010 −0.036 −0.021 −0.032

−1.932 −3.186 −2.902 −3.199

Age × Low Income −0.086 −0.055 −0.066 −0.084

−12.142 −7.460 −9.196 −12.794

Age × Low Education 0.001 −0.014 −0.030 −0.024

0.108 −2.500 −4.140 −3.060

Number of Individuals 22,153 21,777 21,904 22,215

Adjusted R2 0.249 0.211 0.245 0.341

The dependent variable is a measure of cognitive ability. The combined cognitive ability measure is the equal-

weighted measure of the verbal, quantitative, and memory measures. Among the independent variables, Wealth

is the total net-worth of the household including real-estate; Income is the total household income; Age is the

age of the individual, Education is a categorical variable that denotes the level of education from pre-primary to

post-tertiary; Low Income dummy is set to one for investors who are in the lowest income quintile; Low Education

dummy is set to one for investors who are in the lowest education quintile; Over 70 Dummy is set to one for

individuals with age over 70. The t-statistics for the coefficient estimates are shown in smaller font below the

estimates. We winsorize all variables at their 0.5 and 99.5 percentile levels and the independent variables have

been standardized. The household data are from the 2005 wave of the Survey of Health, Aging, and Retirement

in Europe (SHARE).

62

TABLE VI. – ROBUSTNESS TEST RESULTS

Robustness Test Age Experience Age×Hisp Age×AfrAm Age×LowInc Age×LowEdu

(1) 5-Day PTBSD −0.081 0.054 −0.018 −0.037 0.015 −0.041

−2.682 2.134 −1.704 −1.446 0.581 −1.253

(2) 10-Day PTBSD −0.153 0.082 −0.016 −0.018 −0.038 −0.071

−3.790 2.430 −1.469 −1.537 −1.882 −1.621

(3) GH1 Measure −0.023 0.036 −0.042 0.011 −0.020 −0.009

−1.912 3.469 −4.002 1.071 −1.883 −1.672

(4) GH2 Measure −0.010 0.004 −0.010 0.006 −0.005 −0.002

−2.710 2.359 −3.124 0.827 −1.434 −1.536

(5) Alternative Exp. Measure −0.054 0.033 −0.024 −0.004 −0.028 −0.003

−3.690 2.390 −2.087 −0.458 −1.836 −1.381

(6) Internet Users Sub-Sample −0.063 0.048 −0.022 −0.005 −0.025 −0.014

−3.168 2.653 −1.795 −1.161 −1.893 −1.349

(7) 1991-93 Sub Sample −0.041 0.035 0.001 0.011 −0.011 −0.010

−4.739 3.769 0.520 1.137 −2.050 −1.850

(8) 1994-96 Sub Sample −0.034 0.030 −0.021 −0.014 −0.005 −0.007

−2.064 3.672 −2.767 −1.903 −1.698 −1.740

(9) Local Four-Factor Alpha −0.039 0.026 −0.037 −0.021 −0.008 −0.009

−2.738 2.504 −3.408 −1.921 −0.757 −0.702

(10) Eight-Factor Alpha −0.047 0.022 −0.023 0.009 −0.017 −0.004

−3.745 2.314 −3.652 1.124 −2.668 −1.439

(11) Investors With Large Portf −0.053 0.018 −0.032 0.007 −0.032 0.001

−4.759 1.996 −3.268 0.768 −3.099 0.088

(12) Exclude Investors From CA −0.044 0.017 −0.029 0.016 −0.032 −0.003

−2.797 2.651 −2.732 0.532 −3.006 −1.197

This table reports the skill regression estimates using the baseline specification from Table IV, Panel A. The

dependent variable is an investment skill measure. For brevity, we only report the estimates for the variables

that are related to our main hypotheses. The estimates for the control variables are suppressed. In tests (1) and

(2), we use a trading based skill measure, which is defined as the k-day post-trade buy-sell return differential

(PTBSD(k)), k = 5, 10. In tests (3) and (4), we consider the two Graham-Harvey market timing measures

(GH1 and GH2). To compute GH1, the S&P 500 futures index is levered up or down to match the volatility

63

of the investor portfolio. GH1 is the difference between the mean return of the investor portfolio and the mean

return of the volatility-matched market portfolio. GH2 is computed by levering up or down each investor’s

portfolio to match the volatility of the S&P500 futures index. GH2 is the difference between the mean return

of the volatility-matched portfolio and the return of the S&P500 futures index. In both cases, the volatilities

are computed for the time-period in which an investor is active and the investor portfolio is levered up or down

by combining it with T-bills. In test (5), we use an alternative experience measure defined using self-reported

investment experience and knowledge measures. In test (6), we only consider a sub-sample of investors who have

used the Internet to execute trades. Tests (7) and (8) estimate the skill regression for two sub-periods, where the

mean characteristic-adjusted portfolio return is the skill measure. In test (9), we use the local four-factor alpha

as a measure of investment skill. To compute the local four-factor alpha, we consider the performance of the

local part of the investor portfolio that contains stock investments in firms located within a 100 mile radius of

investor’s location. In test (10), the skill measure is the eight-factor alpha. It is the intercept from an eight-factor

model that contains the four commonly used risk factors (RMRF, SMB, HML, and UMD), three industry factors

(Pastor and Stambaugh (2002)), and a liquidity factor (Pastor and Stambaugh (2003)). In test (11), we consider

a sub-sample of investors with large portfolios relative to income. Last, in test (12), we exclude investors who are

located in California. We use the four-factor alpha as the measure of investment skill in tests (5), (6), (11), and

(12). The t-statistic for the coefficient estimates are shown in smaller font below the estimates, where robust,

clustered standard errors are used to account for potential cross-sectional dependence within zip codes.

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FIGURE 1. – AGE, PORTFOLIO PERFORMANCE, AND CHANGE IN PERFORMANCE

Below 32 32−36 36−40 40−44 44−48 48−52 52−56 56−64 64−72 Above 72−4

−3

−2

−1

0

1

2

3

AGE

Annual

Chara

cte

rist

ic−

Adju

sted P

erf

orm

ance L

evel

and D

iffe

renti

al

Performance Level

Performance Differential

This figure shows the risk-adjusted performance level (annualized characteristic-adjusted percentage return) andthe performance differential, conditional upon age. The performance differential is the change in the performancebetween the last three and the first three years of the sample period.

FIGURE 2. – COGNITIVE AGING, PORTFOLIO SIZE, AND PORTFOLIOPERFORMANCE

All Small (Below $10K) Medium ($10K−$50K) Large (Above $50K)−3

−2

−1

0

1

2

3

4

5

6

Portfolio Size

Annual

Ris

k−

Adju

sted P

erf

orm

ance

Low Cognitive Ability

High Cognitive AbilityHigh Minus Low

This figure shows the risk-adjusted performance (annualized characteristic-adjusted percentage return), condi-tional upon portfolio size and investors’ predicted cognitive abilities. The empirical model of cognitive abilitiesestimated in Table V is used to obtain the predicted cognitive ability measures. We regress the predicted cogni-tive ability measure on investment experience and obtain a residual cognitive ability measure that is orthogonalto experience.

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